Kinetic Ising model in two and three dimensions with constraints

Abstract

We present the dynamics of the kinetically constrained Ising model, comprised of a system of spins coupled with the strength J and situated in a field which plays the role of activation energy. Due to kinetic constraints, glassy effects arise at low temperatures leading to a non-Arrhenius α -relaxation time. The results of Monte Carlo simulations are presented for the 2D and 3D facilitated kinetic Ising model with nonzero coupling J. The spin autocorrelation function exhibits, in a broad intermediate time regime, a pronounced stretched exponential decay characterized by an exponent γ . Whereas the relaxation time depends strongly on the activation energy and the interaction strength J, we find a non-universal stretching exponent γ depending on the temperature and on J. In 3D the autocorrelation function shows a crossover into a pure exponential decay consistent with theoretical predictions. The magnetization is also analyzed and identified as a control parameter of the system.

Hydrodynamics in kinetically constrained lattice-gas models

“…By construction, the equilibrium state of these models is trivial. However their dynamics are cooperatively slow and they exhibit many hallmarks of glassy systems, such as dynamical heterogeneities [3][4][5][6][7][8][9][10][11][12][13][14], nonexponential relaxation [8][9][10][11][12][13][14][15][16][17][18][19][20], and ageing [21][22][23], and in certain situations may exhibit an ergodicity-breaking jamming transition, beyond which a finite fraction of the particles are permanently frozen [24][25][26][27][28].…”

Relation between structure of blocked clusters and relaxation dynamics in kinetically constrained models

“…In most previous works regarding the FA and KA models, the relaxation time was measured by the two-time density autocorrelation function [34][35][36][37][38][39][40]. In this paper we use the persistence function, defined as the fraction of particles that have not yet moved until time t (in lattice-gas models) or the fraction of sites that have not changed state until time t (in spin-facilitated models).…”