Critical exponents and marginality of the four-state Potts model: Monte Carlo renormalization group

Abstract

The thermal critical exponent of the four-state Potts model in two dimensions is evaluated as ${\nu }^{-1\mathrm{}}=1.49\mathrm{}\pm 0.01$, using the Monte Carlo renormalization-group method. The presence of a marginal scaling direction is also indicated. These results confirm previous conjectures, universality, and logarithmic corrections. A purely Potts Hamiltonian is considered. A four-point interaction is used to control the chemical potential of effective vacancies, without the introduction of explicit vacancy states.