Deterministic Equations of Motion and Dynamic Critical Phenomena

B. Zheng; M. Schulz; S. Trimper

doi:10.1103/physrevlett.82.1891

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arXiv · cond-mat/9909322

Deterministic Equations of Motion and Dynamic Critical Phenomena

B. Zheng·M. Schulz·S. Trimper

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Abstract

Taking the two-dimensional $ϕ^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the solutions generate a microcanonical ensemble of the system, we demonstrate that the second order phase transition point can be determined already from the short-time dynamic behavior. Initial increase of the magnetization and critical slowing down are observed. The dynamic critical exponent z, the new exponent $θ$ and the static exponents $β$ and $ν$ are estimated. Interestingly, the deterministic dynamics with random initial states is in a same dynamic universality class of Monte Carlo dynamics.

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BibTeX RIS

B. Zheng, M. Schulz, S. Trimper. 1999-09-22. Deterministic Equations of Motion and Dynamic Critical Phenomena. https://doi.org/10.1103/physrevlett.82.1891

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