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Nuclear Physics B

Critical behavior of the two-dimensional random q-state Potts model by expansion in (q − 2)

Andreas W. W. Ludwig

Published Jan 1, 1987• 141 citations
Publisher
DOI
10.1016/0550-3213(87)90330-0

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We study the critical behavior of the q-state Potts model in the presence of quenched random fields, which locally prefer ordering of any one of the q states, and are long-range correlated such that [H(0)H(R${)]}_{\mathrm{av}\mathrm{\ensuremath{\sim}}{R}^{\mathrm{\ensuremath{-}}(d\mathrm{\ensuremath{-}}\ensuremath{\theta})}}$. We find a stable critical behavior controlled by a new random fixed point, and obtain a set of critical exponents within the \ensuremath{\epsilon}\ifmmode \tilde{}\else \~{}\fi{} expansion (\ensuremath{\epsilon}\ifmmode \tilde{}\else \~{}\fi{}=8+\ensuremath{\theta}-d), which cannot be related to those of a pure Potts model of lower dimensionality.
The critical behavior of the three-dimensional random-bond Potts models with many states ( and ) is studied by the finite-time dynamic method. We evaluate the static and dynamic critical exponents as well as the critical temperatures. The asymptotic critical behavior for is identified with , and but the exponents obtained for with are the only effective ones. Our results support that is positive and the intrinsic can escape the bound suggested by previous work. By comparing with the results for various , we infer that the asymptotic critical behavior of the three-dimensional random-bond Potts model with many states is -dependent.