Dynamic critical exponents for Swendsen–Wang and Wolff algorithms obtained by anonequilibrium relaxation method

Abstract

Using a nonequilibrium relaxation method, we calculate the dynamic critical exponentz of the two-dimensional Ising model for the Swendsen–Wang and Wolffalgorithms. We examine dynamic relaxation processes following a quenchfrom a disordered or an ordered initial state to the critical temperatureTc, and measure the exponential relaxation time of the system energy. For theSwendsen–Wang algorithm with an ordered or a disordered initial state,and for the Wolff algorithm with an ordered initial state, the exponentialrelaxation time fits well to a logarithmic size dependence up to a lattice sizeL = 8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponentzexp = 1.19(2) upto L = 2048. For comparison, we also compute the effective dynamic exponents through the integratedcorrelation times. In addition, an exact result of the Swendsen–Wang dynamic spectrum ofa one-dimensional Ising chain is derived.