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Physica A Statistical Mechanics and its Applications

Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis

Henk W. J. Blöte, M. P. Nightingale

Published Jun 1, 1982• 277 citations
Publisher
DOI
10.1016/0378-4371(82)90187-x

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The analysis of renormalisation group equations for the q-state Potts model in two dimensions is generalised to include the presence of a surface field H s besides the bulk one, H B . Combined with conformal invariance results, this allows prediction of a surface susceptibility behaviour delta 2/f delta H s delta H B approximately L -1/8 (1-C'lnL) 15/16 for a q=4 system of size L at the critical temperature. This prediction is checked by a Monte Carlo based finite-size scaling analysis, which also nicely reproduces the exact and conjectured magnetic surface exponents for q=2 and 3, respectively. For the Baxter-Wu model similar methods give results consistent with the q=4 behaviour without logarithmic corrections (c'=0).

Journal of Physics A Mathematical and General•Jul 11, 1987•11 citations
The analysis of renormalisation group equations for the q-state Potts model in two dimensions is generalised to include the presence of a surface field H s besides the bulk one, H B . Combined with conformal invariance results, this allows prediction of a surface susceptibility behaviour delta 2/f delta H s delta H B approximately L -1/8 (1-C'lnL) 15/16 for a q=4 system of size L at the critical temperature. This prediction is checked by a Monte Carlo based finite-size scaling analysis, which also nicely reproduces the exact and conjectured magnetic surface exponents for q=2 and 3, respectively. For the Baxter-Wu model similar methods give results consistent with the q=4 behaviour without logarithmic corrections (c'=0).