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arXiv:cond-mat/9607013 · Physical Review Letters

Generalized Dynamic Scaling for Critical Relaxations

Bo Zheng

Published Jul 22, 1996• 47 citations
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Abstract

The dynamic relaxation process for the two dimensional Potts model at criticality starting from an initial state with very high temperature and arbitrary magnetization is investigated with Monte Carlo methods. The results show that there exists universal scaling behavior even in the short-time regime of the dynamic evolution. In order to describe the dependence of the scaling behavior on the initial magnetization, a critical characteristic function is introduced.

DOI
10.1103/physrevlett.77.679

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The dynamic relaxation process for the two dimensional Potts model at criticality starting from an initial state with very high temperature and arbitrary magnetization is investigated with Monte Carlo methods. The results show that there exists universal scaling behavior even in the short-time regime of the dynamic evolution. In order to describe the dependence of the scaling behavior on the initial magnetization, a critical characteristic function is introduced.
Critical scaling and universality in short-time dynamics for spin models on a twodimensional triangular lattice are investigated by using Monte Carlo simulation. Emphasis is placed on the dynamic evolution from fully ordered initial states to show that universal scaling exists already in the short-time regime in form of power-law behavior of the magnetization and Binder cumulant. The results measured for the dynamic and static critical exponents, θ, z, β and ν, confirm explicitly that the Potts models on the triangular lattice and square lattice belong to the same universality class. Our critical scaling analysis strongly suggests that the simulation for the dynamic relaxation can be used to determine numerically the universality.
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We have carried out extensive computer simulations of the dynamic critical behavior of L\ifmmode\times\else\texttimes\fi{}L q-state Potts models for q=2, 3, and 4. We fit the equilibrium relaxation functions for energy and order parameter to a sum of exponential decays and use the finite-size dependence at Tc{T}_{c}Tc​, \ensuremath{\tau}\ensuremath{\propto}Lz{L}^{z}Lz, to extract estimates for z. We find for the longest relaxation time for both energy and for order parameter that z=2.17\ifmmode\pm\else\textpm\fi{}0.04 describes all three values of q. Our results support the dynamic generalization of the ``weak universality'' hypothesis proposed by Suzuki.