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

Department of Physics, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan

Laboratory of Theoretical Physics and Information Science, Tokuyama University, Gakuendai, Shyunan, Yamaguchi 745-8566, Japan

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KAZUYA YUASA

Waseda Institute for Advanced Study, Waseda University, Tokyo 169-8050, Japan

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NOZOMU HATTORI

Department of Physics, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan

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https://doi.org/10.1142/S0129183109013959Cited by:0 (Source: Crossref)

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.

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