Related papers: Transfer operator analysis of the parallel dynamic…

In this article we address a well known problem at the intersection of ergodic theory and statistical mechanics. We prove that there exists a continuous eigenfunction for the transfer operator corresponding to pair potentials that satisfy a…

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…

We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Applying the mathematical circulation theory of Markov chains, we investigate the synchronized stochastic dynamics of a discrete network model of yeast cell-cycle regulation where stochasticity has been kept rather than being averaged out.…

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp…

The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…

The two dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with well defined frequency and wavelength) is studied by Mone Carlo simulation. This study differs from all of the earlier studies done so…

The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our…

We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…

We extend the work of Tanase-Nicola and Kurchan on the structure of diffusion processes and the associated supersymmetry algebra by examining the responses of a simple statistical system to external disturbances of various kinds. We…

Identifying coherent flow structures in chemical reactors is crucial for understanding the mixing dynamics, which is essential for optimizing reactor performance. We demonstrate the use of a transfer operator method to find coherent flow…

The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability $p$. We find that in contrast to the sparsely…

There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…

We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…

Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the…

A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the…

The dissipative variant of the Ising model in a transverse field is one of the most important models in the analysis of open quantum many-body systems, due to its paradigmatic character for understanding driven-dissipative quantum phase…

Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…

We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do…