Universality and tricritical behavior of three-dimensional Ising models with two- and four-spin interactions

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-½ Ising model on an fcc lattice with mixtures of two- ($J_2$) and four - ($J_4$) spin interactions. In the limit $J_2=0\mathrm{}$ the model exhibits a first-order transition. The transition remains of first order for $\frac{J_4}{J_2}\gtrsim \frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{J_4}{J_2}\approx \frac{1}{4}-\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{J_4}{J_2}\lesssim \frac{1}{4}$, the critical exponent $\beta$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.