Nonequilibrium behaviors of 3D Heisenberg model in the Swendsen-Wang algorithm

TL;DR

This paper investigates the nonequilibrium critical relaxation of the 3D Heisenberg model using the Swendsen-Wang algorithm, revealing stretched-exponential growth and consistent critical exponents, extending previous findings from the 2D Ising model.

Contribution

It extends the universal scaling scheme for nonequilibrium relaxation from the 2D Ising model to the 3D Heisenberg model using the Swendsen-Wang algorithm.

Findings

Critical ordering follows stretched-exponential growth.

Critical exponents are consistent with previous studies.

The scaling scheme effectively describes nonequilibrium relaxation.

Abstract

Recently Y. N. showed that the nonequilibrium critical relaxation of the 2D Ising model from the perfectly-ordered state in the Wolff algorithm is described by the stretched-exponential decay, and found a universal scaling scheme to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. In order to evaluate the critical temperature and critical exponents precisely with the above scaling scheme, we calculate the nonequilibrium ordering from the perfectly-disordered state in the Swendsen-Wamg algorithm, and find that the critical ordering process is described by the stretched-exponential growth with the comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies.