On ergodic relaxation time in the three-dimensional Ising model

  • R. Grigalaitis
  • S. Lapinskas
  • J. Banys
  • E. E. Tornau
Keywords: Ising model, classical Monte Carlo simulations, finite size scaling, ergodic relaxation time

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, τe, of a finite domain below the phase transition temperature Tc was mostly considered for two types of phase transition dynamics. A study of the scaling properties of τe 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 (τe ~ Lz exp [const(Lєν)2], where z and ν are the dynamical and correlation length exponents, respectively, and є = 1 – T/Tc), the ergodic relaxation time for open boundary conditions is proportional to Lz exp [const(Lєν)2k] with coeffcient k for lattices explored in this work slightly decreasing with L in between 1.65 and 1.58. This result implies that only the lattices of sizes close to or exceeding L = 300 with open boundary conditions might have ergodic relaxation times similar to those with perodic boundary conditions.
Published
2013-10-16
Section
Condensed Matter Physics and Technology