Related papers: Phase transitions and random matrices
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon…
We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of…
After surveying the quantum kinematics and dynamics of statistical transmutation, I show how this concept suggests a phase diagram for the two-dimensional matter in a magnetic field, as a function of quantum statistics. I discuss the…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
I review in this chapter several classes of quantum phase transitions that occur in quasi-one dimensional systems. I start by examining the simple case of coupled spin chains and ladders, then move to the case of bosons, and finally deal…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a…
We study phase transformations in finite nuclei as a function of interaction parameters. The signature of a transition is given by invariant correlational entropy that reflects the sensitivity of an individual many-body state to changes of…
In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin…
An elementary method of determination of the character of the hot phase transition in 4d four-fermion NJL-type models is applied to non-supersymmetric and supersymmetric versions of simple NJL model. We find that in the non-susy case the…
We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…