arXiv subjects

Sumedha

Publications and source records attributed to Sumedha.

At least 19 recordsLinked to original sources

arXiv2026

Disorder induced time crystal in athermal random field Ising model with non-reciprocal interactions

A two species random field Ising model with non-reciprocal interactions between the species is studied using the greedy Glauber dynamics. By solving the dynamics exactly on a complete graph, we obtain the phase diagram of the model as a function of the non-reciprocal interaction ($K$) and the variance ($\sigma$) of the quenched random field distribution. The model exhibits a rich phase diagram with the presence of a chaotic time-oscillatory phase for intermediate values of $K$ and $\sigma$. The chaotic phase has stable time oscillations along with the autocorrelation time that diverges with system size on a complete graph and also in three dimensions. We find that the random field disorder along with non-reciprocal interaction alone can produce a time crystal without an external driving. In two dimensions the autocorrelation time does not increase with the system size and the time crystal phase is absent.

cond-mat.stat-mech↗

arXiv2026

Free energy landscape of Dense Associative Memory

Using large deviations theory, we solve and obtain a general expression for the free energy functional for a broad class of associative memories, including dense associative memories. We illustrate the method by reproducing classical results for the Hopfield model. For a finite number of patterns, we derive the temperature-dependent free energy functional for dense associative memories featuring polynomial interactions and Log-Sum-Exponential (LSE) activation. We also evaluate the disorder-averaged ground-state energy of these systems in the extensive limit. Our analytical framework reveals how memory retrieval depends on the initial state in higher-order dense networks, and gives the exact full-retrieval threshold for the LSE model. This method provides a systematic procedure for analyzing diverse, complex architectures in associative memory.

cond-mat.dis-nn↗

arXiv2026

Glauber dynamics phase transitions in athermal random field Blume-Capel and Blume-Emery-Grifitths models

We solve the two models for Glauber dynamics and in equilibrium, both in the presence and absence of the external magnetic field on a complete graph. We compare the steady state of the Glauber dynamics with equilibrium and find that for low values of variance $R$ of the Gaussian random field, the steady state of the Glauber dynamics depends on the initial state. Beyond a critical value $R_{c}$ the equilibrium and non equilibrium steady states coincide. The variance $R$ in random field models behaves similar to the temperature. The location of both the continuous and first order transitions can be obtained exactly for the Glauber dynamics steady state. The frustration is introduced by considering repulsive bi-quadratic interaction for Blume-Emery-Griffiths model. We also. consider repulsive bi-quadratic interaction and show that $R_c$ can become zero depending on the value of the crystal field. Interestingly, we also find that even when a system has $R_c=0$ at the start of quasi-static evolution with Glauber dynamics, with increasing $R$, in some regime of the couplings, the model undergoes a crossover to a random field Ising model universaility with $R_c$ changing from $0$ to $\sqrt{\frac{2}{\pi}}$. In the presence of uniform magnetic field, regions of first order transition exhibit hysteresis under Glauber dynamics. These models exhibit rectangular, hexagonal, parallelogram, wasp-waisted, and double hysteresis loops. We derive the shapes of hysteresis loops analytically giving the equation for the value of the coercive field and show that while the area under the hysteresis loop depends on $R$, the shape is determined by the behavior of the models at $R=0$. In particular, in the case of Blume-Emery-Griffiths model the hysteresis plots have regions of continuous and first order transitions both, resulting in a rich phase diagram that depends non-trivially on the initial state.

cond-mat.stat-mech↗

arXiv2025

Discontinuity in the distribution of field increments between avalanches in non-abelian random field Blume-Emery-Griffiths model with no passing violation

We study the zero-temperature quasi-statically driven dynamics of the random field Blume--Emery--Griffiths model (RFBEGM) as a minimal framework to investigate the consequences of violating the no-passing property in driven disordered systems. While the random field Ising model obeys no-passing and displays abelian relaxation dynamics, we show that this property is generically violated in the RFBEGM. By systematically exploring the full parameter space of the fully connected model, we identify the regimes in which no-passing is broken and demonstrate that, when this violation is combined with frustration induced by a repulsive biquadratic coupling, it leaves a clear dynamical signature. Specifically, the distribution of the minimal field increment required to trigger successive avalanches develops a discontinuity that is absent both in no-passing dynamics and in unfrustrated no-passing-violating regimes. We provide analytical arguments that locate the onset of this discontinuity, in excellent agreement with numerical simulations. Our results establish this discontinuity as a robust diagnostic of frustration-induced blocking in non-abelian avalanche dynamics within a mean-field setting, without making claims about new universality classes.

cond-mat.stat-mech↗

arXiv2025

On the Complexity of Telephone Broadcasting: From Cacti to Bounded Pathwidth Graphs

In the Telephone Broadcasting problem, the goal is to disseminate a message from a given source vertex of an input graph to all other vertices in the minimum number of rounds, where at each round, an informed vertex can send the message to at most one of its uninformed neighbors. For general graphs of n vertices, the problem is NP-complete, and the best existing algorithm has an approximation factor of O(log n/ log log n). The existence of a constant factor approximation for the general graphs is still unknown. In this paper, we study the problem in two simple families of sparse graphs, namely, cacti and graphs of bounded pathwidth. There have been several efforts to understand the complexity of the problem in cactus graphs, mostly establishing the presence of polynomial-time solutions for restricted families of cactus graphs. Despite these efforts, the complexity of the problem in arbitrary cactus graphs remained open. We settle this question by establishing the NP-completeness of telephone broadcasting in cactus graphs. For that, we show the problem is NP-complete in a simple subfamily of cactus graphs, which we call snowflake graphs. These graphs not only are cacti but also have pathwidth 2. These results establish that, despite being polynomial-time solvable in trees, the problem becomes NP-complete in very simple extensions of trees. On the positive side, we present constant-factor approximation algorithms for the studied families of graphs, namely, an algorithm with an approximation factor of 2 for cactus graphs and an approximation factor of O(1) for graphs of bounded pathwidth.

cs.DS↗

arXiv2024

Three state random energy model

We introduce a spin-1 version of the random energy model with crystal field. Crystal field controls the density of 0 spins in the system. We solve the model in the micro-canonincal ensemble. The model has a spin-glass transition at a finite temperature for all strengths of the crystal field. By introducing the magnetic field we also obtain the de Almeida Thouless line for the model. The spin-glass transition persists in the presence of external field. We also find that the magnetisation shows non-monotonic behaviour for high positive crystal field strengths. The zero magnetic field specific heat and magnetic susceptibility also exhibit a cusp beyond a threshold value of the crystal field.

cond-mat.dis-nn↗

arXiv2023

Inverse transitions and disappearance of the {\lambda}-line in the asymmetric random field Ising and Blume-Capel models

We report on reentrance in the random field Ising and Blume-Capel models, induced by an asymmetric bimodal random field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the {\lambda}-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first order transition lines that always end at ordered critical points. We find that while for symmetric random field distributions there was no reentrance, the asymmetry in the random field results in a range of temperatures for which magnetisation shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first order inverse phase transitions that ends at an inverse ordered critical point. We show that the location of the inverse transitions can be inferred from the ground state phase diagram of the model.

cond-mat.stat-mech↗

arXiv2023

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume-Capel model and the repulsive Blume-Emery-Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

cond-mat.stat-mech↗

arXiv2022

Multiple transitions in an infinite range p-spin random-crystal field Blume Capel model

We study a $p$-spin model with ferromagnetic coupling and quenched random-crystal fields for $p \ge 3$ for spin-1 systems. We find that the model has lines of first order transitions at finite temperature $(T)$ for all $p \ge 3$. For bimodal distribution of the random-crystal field these lines meet at a \emph{triple point} for weak strength of the crystal field $(\Delta)$. Beyond a critical strength of $\Delta$, they do not meet and one of the lines ends at a \emph{critical point} $(T_c)$. Interestingly, we find that on increasing $T$ from $T_c$ keeping other parameters fixed, the system undergoes one more transition which is first order in its character. The system thus exhibits a Gardner like transition for a range of parameters for all finite $p \ge 3$. For $p \to \infty$ the model behaves differently and there is only one random first order transition at $T = 0$.

cond-mat.stat-mech↗

arXiv2022

Phase transitions in the Blume-Capel model with trimodal and Gaussian random fields

We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume-Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transition followed by a first order transition line, meeting at a TCP. The TCP vanishes for higher strength of the random field. In contrast to the trimodal case, in Gaussian case no new phase emerges.

cond-mat.stat-mech↗

arXiv2022

Phase transitions in XY models with randomly oriented crystal fields

We obtain a representation of the free energy of an XY model on a fully connected graph with spins subjected to a random crystal field of strength $D$ and with random orientation $\alpha$. Results are obtained for an arbitrary probability distribution of the disorder using large deviation theory, for any $D$. We show that the critical temperature is insensitive to the nature and strength of the distribution $p(\alpha)$, for a large family of distributions which includes quadriperiodic distributions, with $p(\alpha)=p(\alpha+\frac{\pi}{2})$, which includes the uniform and symmetric bimodal distributions. The specific heat vanishes as temperature $T \rightarrow 0$ if $D$ is infinite, but approaches a constant if $D$ is finite. We also studied the effect of asymmetry on a bimodal distribution of the orientation of the random crystal field and obtained the phase diagram comprising four phases: a mixed phase (in which spins are canted at angles which depend on the degree of disorder), an $x$-Ising phase, a $y$-Ising phase and a paramagnetic phase, all of which meet at a tetra-critical point. The canted mixed phase is present for all finite $D$, but vanishes when $D \rightarrow \infty$.

cond-mat.stat-mech↗

arXiv2021

Hysteresis and return point memory in the random field Blume Capel model

We study the zero temperature steady state of the random field Blume Capel model with spin-flip Glauber dynamics on a random regular graph. The magnetization m as a function of the external field H is observed to have double hysteresis loops with a return point memory. We also solve the model on a Bethe lattice in the approximation that the spin relaxation dynamics is abelian and find good agreement between simulations on random regular graphs and Bethe lattice calculations for negative values of H.

cond-mat.stat-mech↗

arXiv2021

Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases

We introduce a rejection-free, flat histogram, cluster algorithm to determine the density of states of hard-core lattice gases. We show that the algorithm is able to efficiently sample low entropy states that are usually difficult to access, even when the excluded volume per particle is large. The algorithm is based on simultaneously evaporating all the particles in a strip and reoccupying these sites with a new appropriately chosen configuration. We implement the algorithm for the particular case of the hard-core lattice gas in which the first k next-nearest neighbors of a particle are excluded from being occupied. It is shown that the algorithm is able to reproduce the known results for k = 1,2,3 both on the square and cubic lattices. We also show that, in comparison, the corresponding flat histogram algorithms with either local moves or unbiased cluster moves are less accurate and do not converge as the system size increases.

cond-mat.stat-mech↗

arXiv2021

Solution of the random field $XY$ magnet on a fully connected graph

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the disorder-averaged ordered state reflects the symmetry of the underlying distribution. The phase boundary has a multicritical point which separates a locus of continuous transitions (for small values of $h$) from a locus of first order transitions (for large $h$). The free energy is a function of a single variable in case (a) and a function of two variables in case (b), leading to different characters of the multicritical points in the two cases. We find that the locus of continuous transitions is given by the same equation for a family of quadriperiodic distributions, which includes the distributions (a) and (b). However, the location of the multicritical point and the nature of ordered state depend on the form of the distribution. The disorder-averaged ground state energy is found exactly, and the specific heat is shown to approach a constant as temperature approaches zero.

cond-mat.stat-mech↗

arXiv2020

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T), crystal field ($\Delta$), and magnetic field (H), is computed on a complete graph, in the canonical and microcanonical ensembles. For weak strength of the biquadratic interaction (K), there exists a tricritical point in the phase diagram where three critical lines meet. As K decreases below a threshold value(which is ensemble dependent), new multicritical points like the critical end point and bicritical end point arise in the (T,$\Delta$) plane. For K>-1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K=-1, the two critical lines in the H plane disappear and as K decreases further, there is no phase transition in the H plane. Exactly at K=-1 the two ensembles become equivalent. Beyond that for all K<-1, there are no multicritical points and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K i.e. for attractive biquadratic interaction. We find that the transition lines in the H plane are not monotonic in temperature for large positive K.

cond-mat.stat-mech↗

arXiv2019

Emergence of a bicritical end point in the random crystal field Blume-Capel model

We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature, crystal field and magnetic field. We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

cond-mat.stat-mech↗

arXiv2018

Conformal Bootstrap Signatures of the Tricritical Ising Universality Class

We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the CFT data of multiple OPEs, we are able to determine the scaling dimension of the spin field $\Delta_\sigma$ in various non-integer dimensions $2 \le d \le 3$. $\Delta_{\sigma}$ is connected to the critical exponent $\eta$ that governs the (tri-)critical behaviour of the two point function via the relation, $\eta = 2 - d + 2 \Delta_{\sigma}$. Our results for $\Delta_\sigma$ match with the exactly known values in two and three dimensions and are a conjecture for non-integer dimensions. We also compare our CFT results for $\Delta_\sigma$ with $\epsilon$-expansion results, available up to $\epsilon^3$ order. Our techniques can be naturally extended to study higher-order multi-critical points.

hep-th↗

arXiv2018

A Stochastic model for dynamics of FtsZ filaments and the formation of Z-ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the $Z$-ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro} observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

q-bio.SC↗