Zero-temperature dynamics of the weakly disordered Ising model

Abstract

The Glauber dynamics of the pure and weakly-disordered random-bond 2dIsing model is studied at zero-temperature. A single characteristic length scale, L(t), is extracted from the equal time correlation function. In the pure case, the persistence probability, P (t), decreases algebraically with the coarsening length scale.In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that P (t) ∼ L(t) −θ ′ , where θ ′ = 0.420 ± 0.009.The value of θ ′ is consistent with that found for the pure 2d Ising model at zero-temperature.Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, P (t) ∼ (ln t) −θ d , where θ d = 0.63 ± 0.01.

Scaling and persistence in the two-dimensional Ising model

“…Hence, in the non-equilibrium dynamics of spin systems at zero-temperature we are interested in the fraction of spins, P (t), that persist in the same state as at t = 0 up to some later time t. For the pure ferromagnetic two-dimensional Ising model, P (t) has been found to decay algebraically [1][2][3][4] P (t) ∼ t −θ (1) where θ = 0.209 ± 0.002 [5]. Similar algebraic decay has been found in numerous other systems displaying persistence [9].…”

“…The 'persistence' problem has attracted considerable interest in recent years [1][2][3][4][5][6][7][8][9]. In its most general form, it is concerned with the fraction of space which persists in its initial state up to some later time.…”

“…Each simulation run begins at t = 0 with a random (±1) starting configuration of the spins and then we update the lattice via single spin flip zero-temperature Glauber dynamics [5].…”

Persistence in a Random Bond Ising Model of Socio-Econo Dynamics

“…It has been only fairly recently established that systems containing disorder [8][9][10] exhibit different persistence behaviour to that of pure systems. A key finding [8][9]11] is the appearance of 'blocking' regardless of the amount of disorder present in the system.…”

“…A key finding [8][9]11] is the appearance of 'blocking' regardless of the amount of disorder present in the system. 'Blocked' spins are effectively isolated from the behaviour of the rest of the system in the sense that they never flip.…”