Deterministic Equations of Motion and Dynamic Critical Phenomena

Taking the two-dimensional φ4 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. PACS: 05.20.-y, 02.60.Cb, 64.60.Ht, 11.10.-z Typeset using REVTEX