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Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation

Jianqing Du·Bo Zheng·Jian-Sheng Wang
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Abstract

With 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 z_exp=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-dimension Ising chain is derived.

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Jianqing Du, Bo Zheng, Jian-Sheng Wang. 2006-03-02. Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation. https://doi.org/10.1088/1742-5468%2F2006%2F05%2Fp05004

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