Dynamic critical exponents for Swendsen-Wang and Wolff algorithms obtained by a nonequilibrium relaxation method

Abstract

Using a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen-Wang and Wolff algorithms. We examine dynamic relaxation processes following a quench from a disordered or an ordered initial state to the critical temperature T c, and measure the exponential relaxation time of the system energy. For the Swendsen-Wang algorithm with an ordered or a disordered initial state, and for the Wolff algorithm with an ordered initial state, the exponential relaxation time fits well to a logarithmic size dependence up to a lattice size L ≤ 8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponent zexp ≤ 1.19(2) up to L ≤ 2048. For comparison, we also compute the effective dynamic exponents through the integrated correlation times. In addition, an exact result of the Swendsen-Wang dynamic spectrum of a one-dimensional Ising chain is derived. © 2006 IOP Publishing Ltd and SISSA.