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Critical Behavior of Random Bond Potts Models

John Cardy·Jesper Lykke Jacobsen
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Abstract

The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple physical explanation of the absence of any latent heat in 2D, and suggests that in higher dimensions such systems should exhibit a tricritical point with a correlation length exponent related to the exponents of the random field model by ν= ν_RF / (2 - α_RF - β_RF). In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a magnetic exponent β/ νwhich varies continuously with q, and a weakly varying correlation length exponent ν\approx 1. We find strong evidence for the multiscaling of the correlation functions as expected for such random systems.

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John Cardy, Jesper Lykke Jacobsen. 1997-05-07. Critical Behavior of Random Bond Potts Models. https://doi.org/10.1103/physrevlett.79.4063

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