Dynamical Critical Exponents of the Four Dimensional Ising Model

Authors: Nevzat AKTEKİN

Abstract: The modified definition of the correlation length for the four dimensional Ising model \xi \propto \epsilon^{-\nu} log^{1/6}\epsilon [1] predicts that the relaxation time for a quantity near the critical temperature T_c should diverge as \tau \propto \epsilon^{-\Delta} log^{\Delta/3}\epsilon where \epsilon, \nu, and \Delta are, respectively, the reduced temperature ( \epsilon=( T_c-T )/T_c, T_c = 6.68 ), the correlation length critical exponent, and a dynamical critical exponent. The \tau-data for the nonlinear relaxation of the order parameter computed on the Creutz cellular automaton [2,3], by using the finite-size lattices of linear dimension L = 12 and 14 as approximations to the infinite lattice for T.

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