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arXiv2011

Thermodynamic Geometry, Phase Transitions, and the Widom Line

We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key theoretical issues in macroscopic thermodynamic constructs, and furthermore characterizes the Widom line through the maxima of the correlation length, which is captured by the thermodynamic scalar curvature. As an illustration of our method, we use it in conjunction with the mean field Van der Waals equation of state to predict the coexistence curve and the Widom line. Where closely applicable, it provides excellent agreement with experimental data. The universality of our method is indicated by direct calculations from the NIST database.

cond-mat.stat-mech↗
arXiv2012

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.

cond-mat.dis-nn↗
arXiv2012

Scale invariant growth processes in expanding space

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behaviour depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lévy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this new approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often non-trivial and random due to amplification of initial fluctuations.

cond-mat.stat-mech↗
arXiv2013

The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices

We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length $k$ on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for $k=7$. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale $ξ^* \gtrsim 1400$, on the square lattice. For distances smaller than $ξ^*$, correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales $\gg ξ^*$. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

cond-mat.stat-mech↗
arXiv2013

Granular Brownian Motors: role of gas anisotropy and inelasticity

We investigate the motion of a wedge-shaped object (a granular Brownian motor), which is restricted to move along the x-axis and cannot rotate, as gas particles collide with it. We show that its steady-state drift, resulting from inelastic gas-motor collisions, is dramatically affected by anisotropy in the velocity distribution of the gas. We identify the dimensionless parameter providing the dependence of this drift on shape, masses, inelasticity, and anisotropy: the anisotropy leads to a dramatic breaking of equipartition, which should easily be visible in experimental realizations.

cond-mat.stat-mech↗
arXiv2013

Ising-like transitions in the O($n$) loop model on the square lattice

We explore the phase diagram of the O($n$) loop model on the square lattice in the $(x,n)$ plane, where $x$ is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For $n>>2$ we find Ising-like phase transitions associated with the onset of a checkerboard-like ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of $n$ represents a softening of its particle-particle potentials. We also determine critical points in the range $-2\leq n\leq 2$. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the $n>2$ transition may continue into the dense phase of the $n \leq 2$ loop model, or continue as a line of $n \leq 2$ O($n$) multicritical points.

cond-mat.stat-mech↗
arXiv2013

Thermal equilibrium in Einstein's elevator

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the Jüttner function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified Jüttner function, which was initially proposed as an alternative to the Jüttner function.

cond-mat.stat-mech↗
arXiv2013

Collective dynamics in systems of active Brownian particles with dissipative interactions

We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbours. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the character of individual motion in our model differ from those in the well-studied Vicsek model, it demonstrates identical statistical properties and phase behaviour.

cond-mat.stat-mech↗
arXiv2013

Chemical-potential route for multicomponent fluids

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Percus-Yevick theory and the associated equation of state is obtained. This Percus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boublík-Mansoori-Carnahan-Starling-Leland equation of state.

cond-mat.stat-mech↗
arXiv2013

Weighted projected networks: mapping hypergraphs to networks

Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise interactions originate from multiway interactions, by starting from ensembles of hypergraphs and applying projections that generate ensembles of weighted projected networks. I calculate analytically the statistical properties of weighted projected networks, and suggest ways these could be used beyond theoretical studies. Weighted projected networks typically exhibit weight disorder along links even for very simple generating hypergraph ensembles. Also, as the size of a hypergraph changes, a signature of multiway interaction emerges on the link weights of weighted projected networks that distinguishes them from fundamentally weighted pairwise networks. This signature could be used to search for hidden multiway interactions in weighted network data. I find the percolation threshold and size of the largest component for hypergraphs of arbitrary uniform rank, translate the results into projected networks, and show that the transition is second order. This general approach to network formation has the potential to shed new light on our understanding of weighted networks.

physics.soc-ph↗
arXiv2013

Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation

We report on the dynamical behavior of defects of strength s = +/- 1/2 in a lyotropic liquid crystal during the annihilation process. By following their positions using time resolved polarizing microscopy technique, we present statistically significant evidence that the relative velocity between defect pairs is Gaussian distributed, anti-persistent and long-range correlated. We further show that simulations of the Lebwohl-Lasher model reproduce quite well our experimental findings.

cond-mat.soft↗
arXiv2013

Non-universal disordered Glauber dynamics

We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the non-universal values of those of plain dimerized chains. In the second situation their values are still non-universal and sub-diffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.

cond-mat.stat-mech↗
arXiv2013

Spectral and formal stability criteria of spatially inhomogeneous stationary solutions to the Vlasov equation for the Hamiltonian mean-field model

Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral stability criterion and the formal stability criterion in the form of necessary and sufficient conditions. These criteria determine stability of spatially inhomogeneous solutions whose stability has not been decided correctly by using a less refined formal stability criterion. It is shown that some of such solutions can be found in a family of stationary solutions to the Vlasov equation, which is parametrized with macroscopic quantities and has a two-phase coexistence region in the parameter space.

cond-mat.stat-mech↗
arXiv2013

Large deviations of cascade processes on graphs

Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical trajectories, which can be crucial for the understanding of the out-of-equilibrium phenomena, is still considered to be intractable in most cases. Here we introduce an efficient method to find and analyze optimized trajectories of cascade processes. We show that for a wide class of irreversible dynamical rules, this problem can be solved efficiently on large-scale systems.

cond-mat.stat-mech↗
arXiv2013

Can car density in a two-lane section depend on the position of the latter in a single-lane road?

We report here results on the study of the totally asymmetric simple exclusion processes (TASEP), defined on an open network, consisting of head and tail simple chain segments with a double-chain section inserted in-between. Results of numerical simulations for relatively short chains reveal an interesting new feature of the network. When the current through the system takes its maximum value, a simple translation of the double-chain section forward or backward along the network, leads to a sharp change in the shape of the density profiles in the parallel chains, thus affecting the total number of cars in that part of the network. In the symmetric case of equal injection and ejection rates (α= β>1/2) and equal lengths of the head and tail sections, the density profiles in the two parallel chains are almost linear, characteristic for the coexistence line (shock phase). Upon moving the section forward (backward), their shape changes to the one typical for the high (low) density phases of a simple chain. The total bulk density of cars in a section with a large number of parallel chains is evaluated too. The observed effect might have interesting implications for the traffic flow control as well as for biological transport processes in living cells. An explanation of this phenomenon is offered in terms of finite-size dependence of the effective injection and ejection rates at the ends of the double-chain section.

cond-mat.stat-mech↗
arXiv2013

Nematic Phase in two-dimensional frustrated systems with power law decaying interactions

We address the problem of orientational order in frustrated interaction systems as a function of the relative range of the competing interactions. We study a spin model Hamiltonian with short range ferromagnetic interaction competing with an antiferromagnetic component that decays as a power law of the distance between spins, $1/r^α$. These systems may develop a nematic phase between the isotropic disordered and stripe phases. We evaluate the nematic order parameter using a self-consistent mean field calculation. Our main result indicates that the nematic phase exists, at mean-field level, provided $0<α<4$. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near $α\sim 0.5$. We also compute a corse-grained effective Hamiltonian for long wave-length fluctuations. For $0<α<4$ the inverse susceptibility develops a set of continuous minima at wave vectors $|\vec k|=k_0(α)$ which dictate the long distance physics of the system. For $α\to 4$, $k_0\to 0$, making the competition between interactions ineffective for greater values of $α$.

cond-mat.stat-mech↗
arXiv2013

Glassy behavior of two-dimensional stripe-forming systems

We study two dimensional frustrated but non-disordered systems applying a replica approach to a stripe forming model with competing interactions. The phenomenology of the model is representative of several well known systems, like high-Tc superconductors and ultrathin ferromagnetic films, which have been the subject of intense research. We establish the existence of a glass transition to a non-ergodic regime accompanied by an exponential number of long lived metastable states, responsible for slow dynamics and non-equilibrium effects.

cond-mat.stat-mech↗