Glauber Critical Dynamics Exact Solution of the Kinetic Gaussian Model.pdfVIP

Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model Jian-Yang Zhua,b,c ∗ and Z. R. Yanga,b a CCAST (World Laboratory), Box 8730, Beijing 100080, China b Department of Physics, Beijing Normal University, Beijing 100875, China† cDepartment of Physics, Jiangxi Normal University, Nanchang 330027,China 2 In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three 0 dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we 0 generalize the spin change mechanism from Glauber’s single-spin flipping to single-spin transition 2 and give a normalized version of the transition probability . We have also investigated the dynamical n critical exponent and found surprisingly that the dynamical critical exponent is highly universal u which refer to that for one- two- and three-dimensions they have same value independent of spatial J dimensionality in contrast to static (equilibrium) critical exponents. 9 2 PACS numbers: 64.60.Ht, 75.10.Hk ] n n - I. INTRODUCTION s i d Irreversible dynamic systems exhibit complicated and interesting non-equilibrium phenomena near the critical point. . t The study of non-equilibrium statistical mechanics is much more difficult than equilibrium state due to the complexity. a However, the interesting dynamic critical behaviors have been attracting a large number of researchers to work hard m for many years. - d Up to now, there is no general theory based on the first princip