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Physica A Statistical Mechanics and its Applications

Nonequilibrium relaxation analysis for first-order phase transitions

Yukiyasu Ozeki, Katsumi Kasono, Nobuyasu Ito, Seiji Miyashita

Published Mar 26, 2003• 31 citations
Publisher
DOI
10.1016/s0378-4371(02)01788-0

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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.
The nonequilibrium relaxation (NER) method is a numerical technique to analyse equilibrium phase transitions. One can estimate the transition point and critical exponents calculating relaxations of order parameter and fluctuations in NER processes from nonequilibrium initial states to the equilibrium ones. It is applied to the second-order transition as well as the first-order one; the precise estimation of transition temperature for the latter case is achieved with the mixed phase initialization technique. Since the equilibration is not necessary in the simulation, one can analyse systems with large sizes which can be recognized as in the thermodynamic limit up to the observation time. This leads to the analysis being more efficient for slowly relaxing systems with frustrations and randomness. It can be extended to the Kosterlitz–Thouless transition and the spin glass transition cases by the use of the finite-time scaling analysis. It is also extended to quantum systems.
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.