Simulation of Relaxation Times Distribution for Relaxors using Distribution of Three-Dimensional Ising-Type Clusters

Abstract

Using n-fold way dynamic algorithm we have studied the dynamical decay of the autocorrelation function of 3D clusters composed of Ising-type dipoles. Trying to reproduce the situation in real ferroelectric materials, we (i) instead of Glauber dynamics, assumed that the spin before the flip has no a priori knowledge of its final energy and (ii) used open boundary conditions assuming that in real experiment, due to existence of impurities, the system consists of finite domains of different sizes. In particular, we followed the behavior of the longest (“ergodic”) relaxation time of a finite domain, the time which is related to flips of a cluster polarization below transition temperature T _c. We found that ergodic relaxation time scales with Lϵ ^ν and is proportional to exp[const(Lϵ ^ν)^3.2]. This result is supported by calculation of surface tension obtained from probability distribution of polarization at T < T _c. Accounting for the contributions of the longest relaxation times, we obtained the relaxation times distribution function characterized by two (sharp and robust) maxima in its relaxation time dependence. Our results qualitatively confirm the assumption that the non-Debye relaxation in dipolar glasses and relaxors might be caused by distribution of sizes of clusters, consisting of ordinary Ising-type dipoles.

Keywords:

• Ising model
• Monte Carlo method
• ergodic time
• autocorrelation function
• distribution of relaxation times

Acknowledgment

This work was supported by the project “Postdoctoral Fellowship Implementation in Lithuania” (No. VP1-3.1-SMM-01-V-01-001).