Nonequilibrium Relaxation Method for First Order Phase Transitions

之康 尾関, Yukiyasu Ozeki

Yukiyasu Ozeki, Katsumi Kasono, Nobuyasu Ito +1 more

Yoshihiko Nonomura, Yusuke Tomita

Yoshihiko Nonomura, Yusuke Tomita

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.

Nobuyasu Ito, S. Fukushima, H. Watanabe +1 more

Michel Pleimling, Ferenc Iglói

We study numerically the nonequilibrium dynamical behavior of an Ising model with mixed two-spin and four-spin interactions after a sudden quench from the high-temperature phase to the first-order phase transition point. The autocorrelation function is shown to approach its limiting value, given by the magnetization in the ordered phase at the transition point, m c , through a stretched exponential decay. On the other hand relaxation of the magnetization starting with an uncorrelated initial state with magnetization, m i , approaches either m c , for m i > 0.5, or zero, for m i < 0.5. For small m i and for m i slightly larger than 0.5 the relaxation of the magnetization shows an asymptotic power law time dependence, thus from a nonequilibrium point of view the transition is continuous.