Critical behaviour of two Ising models with multispin interactions

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 yh close to 158. Direct estimates of the temperature exponent yT 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 32, 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.