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Large-q asymptotics of the random bond Potts model

Jesper Lykke Jacobsen·Marco Picco
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Abstract

We numerically examine the large-q asymptotics of the q-state random bond Potts model. Special attention is paid to the parametrisation of the critical line, which is determined by combining the loop representation of the transfer matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems to behave like c(q) = 1/2 log_2(q) + O(1). Very accurate values of the bulk magnetic exponent x_1 are then extracted by performing Monte Carlo simulations directly at the critical point. As q -> infinity, these seem to tend to a non-trivial limit, x_1 -> 0.192 +- 0.002.

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Jesper Lykke Jacobsen, Marco Picco. 1999-10-06. Large-q asymptotics of the random bond Potts model. https://doi.org/10.1103/physreve.61.r13

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