Article,
Geometric properties of two-dimensional critical and tricritical Potts models
Physical Review E, 69 (2): 026123+ (February 2004)
DOI: 10.1103/physreve.69.026123
Abstract
We investigate geometric properties of the general q-state Potts model in two dimensions, and define geometric clusters as sets of lattice sites in the same Potts state, connected by nearest-neighbor bonds with variable probability p. We find that, besides the random-cluster fixed point, both the critical and the tricritical Potts models have another fixed point in the p direction. For the critical model, the random-cluster fixed point pr is unstable and the other point pg>\~pr is stable; while pr is stable and pg<\~pr is unstable at tricriticality. Moreover, we show that the fixed point pg of a critical and tricritical q-state Potts models can be regarded to correspond to pr of a tricritical and critical q′-state Potts models, respectively. In terms of the coupling constant of the Coulomb gas g, these two models are related as gg′=16. By means of Monte Carlo simulations, we obtain pg=0.6227(2) and 0.6395(2) for the tricritical Blume-Capel and the q=3 Potts model, respectively, and confirm the predicted values of the magnetic and bond-dilution exponents near pg.
