Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the BKT and weak first-order phase transitions

Yoshihiko Nonomura, Yusuke Tomita

Published 2015-09-28Version 1

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential decay of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional (2D) XY model (simple exponential decay) and in the weak first-order phase transition in the 2D $q=5$ Potts model (power-law decay), which means that these phase transitions can clearly be characterized by the present analysis. These relaxation behaviors are compared with those in the 3D and 4D XY models (second-order phase transition) and in the 2D $q$-state Potts models ($2 \le q \le 4$ for second-order and $q \ge 6 $ for strong first-order phase transitions).