Critical behaviour of two Ising models with multispin interactions

Abstract

Abstract We have performed extensive Monte Carlo simulations on the two-dimensional Ising models with n -spin interactions described recently by Debierre and Turban. Results for n = 3 models with sizes up to 128 × 128 are analyzed by means of finite-size scaling. This yields a value of the magnetic exponent y h close to 15 8 . Direct estimates of the temperature exponent y T do not converge convincingly. However, assuming the presence of logarithmic corrections such as in the 4-state Potts model, we obtain an improved estimate of the temperature exponent close to 3 2 , in agreement with 4-state Potts universality. This result is further supported by an exact mapping between the n = 3 model and the 4-state Potts model in an anisotropic limit. For the n = 4 model, we confirm that the phase transition is first order, and we estimate the discontinuities in the energy and the magnetization.