Related papers: The Phase Transition in Statistical Models Defined…
The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
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…
We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…
This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase…
We consider spin-fermion systems which get their magnetic properties from a system of localized magnetic moments being coupled to conducting electrons. The dynamical degrees of freedom are spin-$s$ operators of localized spins and spin-1/2…
We study two versions of the XY model where the spins but also the interaction topology is allowed to change. In the free XY model, the number of links is fixed, but their positions in the network are not. We also study a more relaxed…
Time periodic modulations of the transverse field in the closed XY spin-1/2 chain generate a very rich dynamical phase diagram, with a hierarchy of topological phases characterized by differing numbers of Floquet-Majorana modes. We show…
From general arguments, that are valid for spin models with sufficiently short-range interactions, we derive strong constraints on the excitation spectrum across a continuous phase transition at zero temperature between a magnetic and a…
We consider a many-fermion model which exhibits a transition from a superconducting to a rotational phase with variation of a parameter in its Hamiltonian. The model has analytical solutions in its two limits due to the presence of…
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined…
In this paper we introduce and study a one-parameter family of piecewise analytic interval maps having the tent map and the Farey map as extrema. Among other things, we construct a Hilbert space of analytic functions left invariant by the…
We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…
In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be…
While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
In 1999, Kleban and \"Ozl\"uk introduced a `Farey fraction spin chain' and made a conjecture regarding its asymptotic number of states with given energy, the latter being given (up to some normalisation) by the number $\Phi(N)$ of…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described…
We study phase transition of a nonequilibrium statistical-mechanical model, in which two degrees of freedom with different time scales separated from each other touch to their own heat bath. A general condition for finding anomalous…