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International Journal of Modern Physics C

ANALYSIS OF CRITICAL SHORT-TIME LANGEVIN DYNAMICS IN TWO-DIMENSIONAL ϕ4 THEORY ON THE BASIS OF A HIGHER-ORDER ALGORITHM

Tsuyoshi Otobe, Hiromichi Nakazato, Keisuke Okano, Kazuya Yuasa, Nozomu Hattori

Published May 1, 2009• 0 citations

Abstract

We investigate the critical short-time scaling of the two-dimensional lattice ϕ4 field theory with a Langevin dynamics. Starting from a "hot" initial configuration but with a small magnetization, the critical initial increase of the magnetization is observed, through which we determine the critical point. From the short-time relaxation dynamics of various quantities at the critical point obtained, the dynamic critical exponents θ, z and the static exponent β/ν are evaluated. In executing a Langevin simulation, an appropriate discretization method with respect to the time degree of freedom becomes essentially important to be adopted and we show that the well-known second-order form of discretized Langevin equation works well to investigate the short-time dynamics.

DOI: 10.1142/s0129183109013959

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z

, the new exponent $\ensuremath{\theta}$, and the static exponents $\ensuremath{\beta}$ and $\ensuremath{\nu}$ are estimated. The deterministic dynamics with random initial states is in the same universality class as the Monte Carlo dynamics.

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