Related papers: Parallel simulation of two--dimensional Ising mode…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function $H(\sigma)$. These dynamics turn out to be reversible and their stationary measure…
We implemented a parallel version of the multicanonical algorithm and applied it to a variety of systems with phase transitions of first and second order. The parallelization relies on independent equilibrium simulations that only…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…
Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are…
We studied the critical behavior of the $J_{1}-J_{2}$ spin-{1/2} Ising model in the square lattice by considering $J_{1}$ fixed and $J_{2}$ as random interactions following discrete and continuous probability distribution functions. The…
One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges exhibiting a parity-conserving (PC) phase transition on the level of kinks are…
We investigate the problem of constructing a dynamics on edge--spin configurations which realizes a coupling between a Glauber dynamics of the Ising model and a dynamical evolution of the percolation configurations. We dream of constructing…
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
Using an efficient one and two qubit gate simulator, operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin 1/2 model on a two dimensional lattice, which is periodically driven by a…
We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations…
For distributions over discrete product spaces $\prod_{i=1}^n \Omega_i'$, Glauber dynamics is a Markov chain that at each step, resamples a random coordinate conditioned on the other coordinates. We show that $k$-Glauber dynamics, which…
We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
An Ising spin system under the critical temperature driven by a dichotomous Markov noise (magnetic field) with a finite correlation time is studied both numerically and theoretically. The order parameter exhibits a transition between two…
The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at $T=\infty$ are investigated numerically from the point of view of a phase transition.…
The mixed spin 3- spin 3/2 Ising model has been simulated using cooling algorithm on cellular automaton (CA). The simulations have been made in the interval -6<=D<=6 for J=1 for the square lattices with periodic boundary conditions. The…
We show how a quantum Ising spin chain in a time-dependent transverse magnetic field can be simulated and experimentally probed in the framework of circuit QED with current technology. The proposed setup provides a new platform for…