title: Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions.
abstract: Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.
authors.affiliation: Computational Materials Science Unit, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan.
authors.forename: Yoshihiko
authors.initials: Y
authors.lastname: Nonomura
authors.affiliation: College of Engineering, Shibaura Institute of Technology, Saitama 337-8570, Japan.
authors.forename: Yusuke
authors.initials: Y
authors.lastname: Tomita