ANALYSIS OF CRITICAL SHORT-TIME LANGEVIN DYNAMICS IN TWO-DIMENSIONAL phi(4) THEORY ON THE BASIS OF A HIGHER-ORDER ALGORITHM
We investigate the critical short-time scaling of the two-dimensional lattice phi(4) 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 theta, z and the static exponent beta/nu 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-know second-order form of discretized Langevin equation works well to investigate the short-time dynamics.
langevin dynamics phi(4) theory higher-order algorithm short-time scaling critical phenomena