Partition function of two- and three-dimensional Potts ferromagnets for arbitrary values of q>0

Details Partition function of two- and three-dimensional Potts ferromagnets for arbitrary values of q>0 Partition function of two- and three-dimensional Potts ferromagnets for arbitrary values of q>0

2004-10-22

arxiv.org/abs/cond-mat/0410583v1

Phys. Rev. Lett. 94, 050601 (2005)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, RevTex

Scientific paper

10.1103/PhysRevLett.94.050601

A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with high precision. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the distribution of the case q=1 (graph percolation), where the exact result Z_1=1 is known. As application, d=2 and d=3-dimensional ferromagnetic Potts models are studied, and the critical values q_c, where the transition changes from second to first order, are determined. Large systems of sizes N=1000^2 respectively N=100^3 are treated. The critical value q_c(d=2)=4 is confirmed and q_c(d=3)=2.35(5) is found.

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