On ergodic relaxation time in the three-dimensional Ising model

Abstract

We have studied the dynamical decay of the autocorrelation function of the 3D Ising model for different sizes L = 20-52 of spin cluster-cubes. The behaviour of the longest, ergodic relaxation time, τ e , of a finite domain below the phase transition temperature T c was mostly considered for two types of phase transition dynamics. A study of the scaling properties of τ e demonstrates a negligible difference between the types of dynamics used, but a considerable difference for different boundary conditions. In contrast to the known result for periodic boundary conditions (τ e ~ L z exp [const(Lє

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

“…Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance). After its publication [3], Zhang's conjectured solution has received supports from several groups, for instance, March and his co-workers [32][33][34][35][36], Ławrynowicz and some mathematicians [6,7,37,38], Kaupuzs and his colleagues [30,39,40], and others [41][42][43][44][45][46][47][48][49][50][51][52][53]. In [8], Zhang-Suzuki-March rigorously proved four Theorems, which verifies the correctness of the Zhang's conjectured solution [3].…”