Related papers: Approximation method to metastability: an applicat…
We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price…
We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…
Given a target Gibbs distribution $\pi^0_{\beta} \propto e^{-\beta \mathcal{H}}$ to sample from in the low-temperature regime on $\Sigma_N := \{-1,+1\}^N$, in this paper we propose and analyze Metropolis dynamics that instead target an…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the…
We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…
In this article, we study the hierarchical structure of metastability in the reversible inclusion process. We fully characterize the third time scale of metastability subject to any underlying geometry of the system and prove that this is…
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of zero external magnetic field, using a generalization of the combinatorial method of Feynman and…
The non-equilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of metastable configurations that are…
We study numerically the entanglement entropy and spatial correlations of the one dimensional transverse field Ising model with three different perturbations. First, we focus on the out of equilibrium, steady state with an energy current…
Based on the Robertson theory the nonlinear dynamics of general Ising systems coupled microscopically to bath systems is investigated leading to two complimentary approaches. Within the master equation approach microscopically founded…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths $J_1 > 0$ and $J_2 < 0$, respectively, on the honeycomb lattice. For $J_2 > - J_1 / 4$ it has a…
It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like…
The metastable lifetime of the square-lattice and simple-cubic-lattice kinetic Ising models are studied in the low-temperature limit. The simulations are performed using Monte Carlo with Absorbing Markov Chain algorithms to simulate…
The 3D Ising-like system in the external field is described using the non-perturbative collective variables method. The universal as well as nonuniversal system characteristics are obtained within the framework of this approach. The…
The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the…
We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$…