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.

arXiv:cond-mat/9607013Physical Review LettersJul 22, 199647 citations

The European Physical Journal B

New universal short-time scaling behaviour of critical relaxation processes

H. K. Janssen, Bernd Schaub, B. Schmittmann

Published Dec 1, 1989• 580 citations

Publisher

DOI: 10.1007/bf01319383

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3\mathrm{D}

) clock model, whose critical point has emergent

U(1)

symmetry. We find that in contrast to the magnetization

M

, whose relaxation process is described by the usual dynamic exponent

z

of the

3\mathrm{D}

XY universality class, the angular order parameter ${\ensuremath{\phi}}_{q}$ shows a remarkable two-stage evolution characterized by different dynamic critical exponents. While in the short-time stage the relaxation dynamics is governed by

z

, in the long-time stage the dynamics is controlled by a new dynamic exponent ${z}^{\ensuremath{'}}$. Further scaling analyses confirm that ${z}^{\ensuremath{'}}$ is an indispensable dynamic critical exponent. Our results may be detected in the hexagonal

R{\mathrm{MnO}}_{3}

(

R=\mathrm{rare}

earth) materials experimentally.