Short-time critical dynamics of statistical systems and field theory

N. V. Antonov, A. N. Vasil’ev

H. J. Luo, Lothar Schülke, Bo Zheng

In 1989 Janssen, Schaub and Schmittmann have shown that universality and scaling hold already in the early stage of the dynamical evolution of statistical systems, if the system, initially at a very high temperature, is suddenly quenched to the critical temperature and then released to the dynamic evolution according to model A. This allows for a measurement of all the static and dynamic critical exponents and even for the critical point already in the short-time regime, i.e., far from equilibrium. Since the correlation length is still small here, the simulations do not suffer from critical slowing down, a problem encountered in the usual measurements in equilibrium. The concept has been successfully applied to a variety of statistical systems. We will report about recent results for the fully frustrated XY model, where the short-time approach is particularly efficient, since the standard cluster algorithm does not apply because of the frustration.

知司 山田, Takao Ohta, Kyozi Kawasaki

Alessio Chiocchetta, Marco Távora, Andrea Gambassi +1 more

Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate here the dynamics of an isolated quantum system represented by a scalar ${\ensuremath{\phi}}^{4}$ theory after a global quench of the potential close to a dynamical critical point. We demonstrate that, within a prethermal regime, the time dependence of the relevant correlations is characterized by a short-time universal exponent, which we calculate at the lowest order in a dimensional expansion.

Lothar Schülke, Bo Zheng

Universal short-time behavior of the critical dynamics has been confirmed numerically for some simple statistical models. The critical initial increase of the magnetization has been observed and the new dynamic exponent (theta) has been measured. We report further about a new kind of measurement of all the static exponents and the dynamic exponent z from short- time dynamics.

Richard Bausch, H. K. Janssen, H. Wagner