Numerical investigations of phase transitions and critical phenomena

M.I. Tribel'skii

M. P. Nightingale

Yukiyasu Ozeki, Nobuyasu Ito, 尾関 之康 +1 more

John F. Nagle

Ezequiel Vicente Albano, M. A. Bab, Gabriel Baglietto +6 more

We review recent progress in the understanding of phase transitions and critical phenomena, obtained by means of numerical simulations of the early dynamic evolution of systems prepared at well-specified initial conditions. This field has seen exhaustive scientific research during the last decade, when the renormalization-group (RG) theoretical results obtained at the end of the 1980s were applied to the interpretation of dynamic Monte Carlo simulation results. While the original RG theory is restricted to critical phenomena under equilibrium conditions, numerical simulations have been applied to the study of far-from-equilibrium systems and irreversible phase transitions, the investigation of the behaviour of spinodal points close to first-order phase transitions and the understanding of the early-time evolution of self-organized criticality (SOC) systems when released far form the SOC regime. The present review intends to provide a comprehensive overview of recent applications in those fields, which can give the flavour of the main ideas, methods and results, and to discuss the directions for further studies. All of these numerical results pose new and interesting theoretical challenges that remain as open questions to be addressed by new research in the coming years.

Hendrik Ballhausen

Recent work on exact renormalization group flow equations has pointed out the possibility to study critical phenomena in continuous dimension D of space. In an investigation of the O(N) model the dimension N of the fields may be seen as a continuous parameter as well. One may conjecture that a variation of D or N in the vicinity of a second order phase transition yields the same critical exponents as a variation of the temperature. A numerical computation confirms this.