arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 73 records · Page 4Linked to original sources

arXiv2025

The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study

The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between non-classical and short-range universality classes.In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+σ}$, and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $σ\leq 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a non-zero constant in the form of a power law for $σ< 2$, with decaying exponent $2-σ$, and in the form of the inverse logarithm of distance for $σ=2$. Moreover, the critical points and exponents are also determined for various $σ$. We provide compelling evidence that the crossover between non-classical and short-range regimes occurs at $σ=2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems.

cond-mat.stat-mech↗

arXiv2025

Percolation in the two-dimensional Ising model

The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds, with probability $p$, between any pair of parallel spins within an extended range beyond nearest neighbors. At the Ising criticality, we observe two percolation transitions as $p$ increases: starting from a disordered phase with only small clusters, the percolation system enters into a stable critical phase that persists over a wide range $p_{c_1} < p < p_{c_2}$, and then develops a long-ranged percolation order with giant clusters for both up and down spins. At $p_{c1}$ and for the stable critical phase, the critical behaviors agree well with those for the Fortuin-Kasteleyn random clusters and the spin domains of the Ising model, respectively. At $p_{c2}$, the fractal dimension of clusters and the scaling exponent along $p$ direction are estimated as $y_{h2} = 1.958\,0(6)$ and $y_{p2} = 0.552(9)$, of which the exact values remain unknown. These findings reveal interesting geometric properties of the two-dimensional Ising model that has been studied for more than 100 years.

cond-mat.stat-mech↗

arXiv2025

Matsubara-Frequency-Resolved Spin Exchange-Correlation Kernel for the Three-Dimensional Uniform Electron Gas

The spin Coulomb drag effect, arising from the exchange of momentum between electrons of opposite spins, plays a crucial role in the spin transport of interacting electron systems and can be characterized by the exchange-correlation (XC) kernel in the spin channel $K_{\rm XC}^-(q,ω)$. Using the state-of-the-art Variational Diagrammatic Monte Carlo approach, we compute the Matsubara-frequency-resolved spin XC kernel $K_{\rm XC}^-(q,iω_n)$ for the three-dimensional uniform electron gas at sufficiently low temperatures with high precision. In the long-wavelength limit, we identified a singular behavior of the form $A(iω_n)/q^2$, confirming the theoretically predicted ultranonlocal behavior associated with spin Coulomb drag. Analysis of this structure in the low frequency region enables precise determination of two crucial parameters characterizing the spin Coulomb drag effect: the spin mass enhancement factor and spin diffusion relaxation time. We observe a significant trend of increasing enhancement of the spin mass factor with decreasing electron density, and provide clear evidence for the suppression of spin diffusion at low temperatures. These quantitative findings advance our understanding of Coulomb interaction effects on spin transport and provide essential parameters for time-dependent density functional theory and spintronics applications.

cond-mat.str-el↗

arXiv2025

Finite-size corrections from the subleading magnetic scaling field for the Ising and Potts models in two dimensions

In finite-size scaling analyses of critical phenomena, proper consideration of correction terms, which can come from different sources, plays an important role. For the Fortuin-Kasteleyn representation of the $Q$-state Potts model in two dimensions, although the subleading magnetic scaling field, with exactly known exponent, is theoretically expected to give rise in finite-size-scaling analyses, numerical observation remains elusive probably due to the mixing of various corrections. We simulate the O($n$) loop model on the hexagonal lattice, which is in the same universality class as the $Q=n^2$ Potts model but has suppressed corrections from other sources, and provides strong numerical evidence for the attribution of the subleading magnetic field in finite-size corrections. Interestingly, it is also observed that the corrections in small- and large-cluster-size regions have opposite magnitudes, and, for the special $n=2$ case, they compensate with each other in observables like the second moment of the cluster-size distribution. Our finding reveals that the effect of the subleading magnetic field should be taken into account in finite-size-scaling analyses, which was unfortunately ignored in many previous studies.

cond-mat.stat-mech↗

arXiv2025

Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model

The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature phase transition but instead manifests asymptotic freedom. However, some research has also proposed the possibility of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition over the years. In this study, we revisit the classical two-dimensional (2D) Heisenberg model through large-scale simulations with linear system sizes up to $L=16384$. Our Monte-Carlo data, without any extrapolation, clearly reveal an exponential divergence of the correlation length $ξ$ as a function of inverse temperature $β$, a hallmark of asymptotic freedom. Moreover, extrapolating $ξ$ to the thermodynamic limit in the low-temperature regime achieves close agreement with the three-loop perturbative calculations. We further propose a finite-size scaling (FSS) ansatz for $ξ$, demonstrating that the pseudo-critical point $β_L$ diverges logarithmically with $L$. The thermodynamic and finite-size scaling behaviors of the magnetic susceptibility $χ$ are also investigated and corroborate the prediction of asymptotic freedom. Our work provides solid evidence for asymptotic freedom in the 2D Heisenberg model and advances understanding of finite-size scaling in such systems.

cond-mat.stat-mech↗

arXiv2025

Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions

The number $n_s$ of clusters (per site) of size $s$, a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\simeq s^{-τ}\, A\, (1+B s^{-Ω})$. For the Fortuin--Kasteleyn representation of the $Q$-state Potts model in two dimensions, the Fisher exponent $τ$ is known as a function of the real parameter $0\le Q\le4$, and, for bond percolation (the $Q\rightarrow 1$ limit), the correction-to-scaling exponent is derived as $Ω=72/91$. We theoretically derive the exact formula for the correction-to-scaling exponent $Ω=8/[(2g+1)(2g+3)]$ as a function of the Coulomb-gas coupling strength $g$, which is related to $Q$ by $Q=2+2\cos(2 πg)$. Using an efficient Monte Carlo cluster algorithm, we study the O($n$) loop model on the hexagonal lattice, which is in the same universality class as the $Q=n^2$ Potts model, and has significantly suppressed finite-size corrections and critical slowing-down. The predictions of the above formula include the exact value for percolation as a special case and agree well with the numerical estimates of $Ω$ for both the critical and tricritical branches of the Potts model.

cond-mat.stat-mech↗

arXiv2025

Spreading dynamics of information on online social networks

Social media is profoundly changing our society with its unprecedented spreading power. Due to the complexity of human behaviors and the diversity of massive messages, the information spreading dynamics are complicated, and the reported mechanisms are different and even controversial. Based on data from mainstream social media platforms, including WeChat, Weibo, and Twitter, cumulatively encompassing a total of 7.45 billion users, we uncover a ubiquitous mechanism that the information spreading dynamics are basically driven by the interplay of social reinforcement and social weakening effects. Accordingly, we propose a concise equation, which, surprisingly, can well describe all the empirical large-scale spreading trajectories. Our theory resolves a number of controversial claims and satisfactorily explains many phenomena previously observed. It also reveals that the highly clustered nature of social networks can lead to rapid and high-frequency information bursts with relatively small coverage per burst. This vital feature enables social media to have a high capacity and diversity for information dissemination, beneficial for its ecological development.

physics.soc-ph↗

arXiv2025

Universality of the complete-graph Potts model with $0< q \leq 2$

Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of microscopic details. In a simplest and mean-field treatment--i.e., the Potts model on complete graph (CG), the phase transition is further established to be of percolation universality for the range of $0 < q <2$. By simulating the CG Potts model in the random-cluster representation, we numerically demonstrate such a hyper-universality that the critical exponents are the same for $0< q <2$ and, moreover, the Ising system ($q = 2$) exhibits a variety of critical geometric properties in percolation universality. On the other hand, many other universal properties in the finite-size scaling (FSS) theory, including Binder-like ratios and distribution function of the order parameter, are observed to be $q$-dependent. Our finding provides valuable insights for the study of critical phenomena in finite spatial dimensions, particularly when the FSS theory is utilized.

cond-mat.stat-mech↗

arXiv2025

Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model

Disordered lattice spin systems are crucial in both theoretical and applied physics. However, understanding their properties poses significant challenges for Monte Carlo simulations. In this work, we investigate the two-dimensional random-bond Ising model using the recently proposed Tensor Network Monte Carlo (TNMC) method. This method generates biased samples from conditional probabilities computed via tensor network contractions and corrects the bias using the Metropolis scheme. Consequently, the proposals provided by tensor networks function as block updates for Monte Carlo simulations. Through extensive numerical experiments, we demonstrate that TNMC simulations can be performed on lattices as large as $1024\times 1024$ spins with moderate computational resources, a substantial increase from the previous maximum size of $64\times 64$ in MCMC. Notably, we observe an almost complete absence of critical slowing down, enabling the efficient collection of unbiased samples and averaging over a large number of random realizations of bond disorders. We successfully pinpoint the multi-critical point along the Nishimori line with significant precision and accurately determined the bulk and surface critical exponents. Our findings suggest that TNMC is a highly efficient algorithm for exploring disordered and frustrated systems in two dimensions.

cond-mat.stat-mech↗

arXiv2025

Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model

The Hubbard model at temperatures above the Néel transition, despite being a paramagnet, can exhibit rich physics due to the interplay of Fermi surface, on-site interaction $U$ and thermal fluctuations. Nevertheless, the understanding of the crossover physics remains only at a qualitative level, because of the intrinsically smooth behavior. Employing an improved variant of the {\it numerically exact} auxiliary-field quantum Monte Carlo algorithm equipped with numerical analytic continuation, we obtain a broad variety of thermodynamic and dynamical properties of the three-dimensional Hubbard model at half filling, quantitatively determine the crossover boundaries, and observe that the metal-insulator crossover regime, in which antiferromagnetic spin correlations appear strongest, exists over an extended regime in between the Fermi liquid for small $U$ and the Mott insulator for large $U$. In particular, the location of the most rapid suppression of double occupancy as $U$ increases, is found to fully reside in the metallic Fermi liquid regime, in contrast to the conventional intuition that it is a representative feature for entering the Mott insulator. Beside providing a reliable methodology for numerical study of crossover physics, our work can also serve as a timely and important guideline for the most recent optical lattice experiments.

cond-mat.str-el↗

arXiv2024

Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study

The interplay between quantum and thermal fluctuations can induce rich phenomena at finite temperatures in strongly correlated fermion systems. Here we report a {\it numerically exact} auxiliary-field quantum Monte Carlo (AFQMC) study for the finite-temperature properties of three-dimensional repulsive Hubbard model at half filling. We concentrate on the complete temperature-interaction strength phase diagram of the model, which contains the low-temperature antiferromagnetic (AFM) long-range ordered phase and metal-insulator crossover (MIC) in the paramagnetic phase. Enabling access to unprecedented system sizes up to $20^3$, we achieve highly accurate results of the Néel transition temperature for representative values of on-site interaction $U$ via finite-size analysis of AFM structure factor. To quantitatively characterize the MIC above the Néel transition, we have developed fully new techniques allowing to compute the thermal entropy versus $U$ at fixed temperature and to directly calculate the $U$-derivative of double occupancy in AFQMC simulations. Then combining variously thermodynamic and dynamical observables, we establish an efficient scheme to precisely determine the boundaries for the MIC by cross-checking different observables. We also demonstrate the temperature dependence of many commonly used observables. Away from half filling, we explore the behavior of the sign problem and AFM spin correlation versus hole doping, and demonstrate the persistance of Néel AFM ordered phase to finite doping with limited results.

cond-mat.str-el↗

arXiv2024

Spatial Optical Simulator for Classical Statistical Models

Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock, $XY$, Potts, and Heisenberg models, utilizing a digital micromirror device composed of a large number of tiny mirrors. Spins, with desired amplitudes or phases of the statistical models, are precisely encoded by a patch of mirrors with a superpixel approach. Then, by modulating the light field in a sequence of designed patterns, the spin-spin interaction is realized in such a way that the Hamiltonian symmetries are preserved. We successfully simulate statistical systems on a fully connected network, with ferromagnetic or Mattis-type random interactions, and observe the corresponding phase transitions between the paramagnetic, and the ferromagnetic or spin-glass phases. Our results largely extend the research scope of spatial optical simulators and their versatile applications.

physics.optics↗

arXiv2024

Crossover Finite-Size Scaling Theory and Its Applications in Percolation

Finite-size scaling (FSS) for a critical phase transition ($t=0$) states that within a window of size $|t|\sim L^{-1/ν}$, the scaling behavior of any observable $Q$ in a system of linear size $L$ asymptotically follows a scaling form as $Q(t,L)=L^{Y_Q}\tilde{Q}(tL^{1/ν})$, where $ν$ is the correlation-length exponent, $Y_Q$ is an FSS exponent and ${\tilde Q}(x)$ is a function of the scaled distance-to-criticality $x \equiv tL^{1/ν}$. We systematically study the asymptotic scaling behavior of ${\tilde Q}(|x|\to\infty)$ for a broad variety of observables by requiring that the FSS and infinite-system critical behaviors match with each other in the crossover critical regime with $t \to 0$ and $|x|\to\infty$. This crossover FSS theory predicts that when the criticality is approached at a slower speed as $|t|\sim L^{-λ}$ with $λ<1/ν$, the FSS becomes $λ$-dependent and the exponent can be derived. As applications, explosive percolation and high-dimensional percolation are considered. For the former, it is shown that the widely observed anomalous phenomena at the infinite-system criticality $t=0$ can be attributed to the mixing effects of the standard FSS behaviors around the pseudocritical point in an event-based ensemble. For the latter, FSS exponents are found to be different at the infinite-system critical and the pseudocritical point if free boundary conditions are used, and they are related to each other by using the crossover FSS theory. From these observations, the FSS of percolation systems falls into three classifications. Extensive simulations are carried out to affirm these predictions.

cond-mat.stat-mech↗

arXiv2024

Self-similar gap dynamics in percolation and rigidity percolation

Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in cluster sizes. Surprisingly, we find that the gap sizes follow a universal power-law distribution throughout the whole or a significant portion of process, revealing a previously unrecognized temporal self-similarity. This phenomenon appears across various percolation models, like standard, explosive and rigidity percolation. Furthermore, in rigidity percolation, we directly observe a cascading cluster-merging dynamics, triggered by single bond insertion, and further obtain a distinct temporal self-similarity in the number of merged clusters, which are hidden in static analyses. Our results also suggest that, for rigidity percolation, the temporal self-similarity is probably more intrinsic than the spatial one. These findings offer a fresh perspective on critical phenomena and broaden potential applications across complex systems.

cond-mat.stat-mech↗

arXiv2024

Universal Scaling of Gap Dynamics in Percolation

Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest cluster across various percolation models, spanning from latticebased to network systems, encompassing both continuous and discontinuous percolation. Our results uncover an inherent self-similarity in the dynamical process both for critical and supercritical phase, characterized by two independent Fisher exponents, respectively. Utilizing a scaling ansatz, we propose a novel scaling relation that links the discovered Fisher exponents with other known critical exponents. Additionally, we demonstrate the application of our theory to real systems, showing its practical utility in extracting the corresponding Fisher exponents. These findings enrich our understanding of percolation dynamics and highlight the robust and universal scaling laws that transcend individual models and extend to broader classes of complex systems.

cond-mat.stat-mech↗

arXiv2024

Logarithmic Finite-Size Scaling of the Four-Dimensional Ising Model

Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic correction exponents $(\hat{y}_t, \hat{y}_h)=(1/6,1/4)$. Using high-efficient cluster algorithms and the lifted worm algorithm, we present a systematic study of the FSS of the four-dimensional Ising model in the Fortuin-Kasteleyn (FK) bond and loop representations. Our numerical results reveal the FSS behaviors of various geometric and physical quantities in the three representations, offering robust evidence for the logarithmic correction form conjectured by the field theory. In particular, clear evidence is obtained for the existence of $\hat{y}_t=1/6$ in the loop representation, while it is difficult to extract in the spin representations, because of mixing with the Gaussian-fixed-point asymptotics. In the FK-bond representation, the multiplicative logarithmic correction for the second-largest cluster is also numerically observed to be governed by an exponent $\hat{y}_{h2} = -1/4$ with its exact value unknown yet.

cond-mat.stat-mech↗

arXiv2024

Explosive percolation in finite dimensions

Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors of EP in infinite dimensions (complete graph) can be accurately extracted using the event-based method, with finite-size scaling behaviors still described by the standard finite-size scaling theory. We perform an extensive simulation of EPs on hypercubic lattices ranging from dimensions $d=2$ to $6$, and find that the critical behaviors consistently obey the standard finite-size scaling theory. Consequently, we obtain a high-precision determination of the percolation thresholds and critical exponents, revealing that EPs governed by the product and sum rules belong to different universality classes. Remarkably, despite the mean of the dynamic pseudocritical point $\mathcal{T}_L$ deviating from the infinite-lattice criticality by a distance determined by the $d$-dependent correlation-length exponent, $\mathcal{T}_L$ follows a normal (Gaussian) distribution across all dimensions, with a standard deviation proportional to $1/\sqrt{V}$, where $V$ denotes the system volume. A theoretical argument associated with the central-limit theorem is further proposed to understand the probability distribution of $\mathcal{T}_L$. These findings offer a comprehensive understanding of critical behaviors in EPs across various dimensions, revealing a different dimension-dependence compared to standard bond percolation.

cond-mat.stat-mech↗

arXiv2024

Universality of closed nested paths in two-dimensional percolation

Recent work on percolation in $d=2$ [J. Phys. A {\bf 55} 204002] introduced an operator that gives a weight $k^{\ell}$ to configurations with $\ell$ `nested paths' (NP), i.e. disjoint cycles surrounding the origin, if there exists a cluster that percolates to the boundary of a disc of radius $L$, and weight zero otherwise. It was found that ${\rm E}(k^{\ell}) \sim L^{-X_{\rm NP}(k)}$, and a formula for $X_{\rm NP}(k)$ was conjectured. Here we derive an exact result for $X_{\rm NP}(k)$, valid for $k \ge -1$, replacing the previous conjecture. We find that the probability distribution ${\rm P}_\ell (L)$ scales as $ L^{-1/4} (\ln L)^\ell [(1/\ell!) Λ^\ell]$ when $\ell \geq 0$ and $L \gg 1$, with $Λ= 1/\sqrt{3} π$. Extensive simulations for various critical percolation models confirm our theoretical predictions and support the universality of the NP observables.

cond-mat.stat-mech↗