Constrained tricritical phenomena in two dimensions

Abstract

We investigate several tricritical models on the square lattice by means of Monte Carlo simulations. These include the Blume-Capel model, Baxter's hard-square model, and the q=1 , 3, and 4 Potts models with vacancies. We use a combination of the Wolff and geometric cluster methods, which conserves the total number of vacancies or lattice-gas particles and suppresses critical slowing down. Several quantities are sampled, such as the specific heat C and the structure factor C(s) , which accounts for the large-scale spatial inhomogeneity of the energy fluctuations. We find that the constraint strongly modifies some of the critical singularities. For instance, the specific heat C reaches a finite value at tricriticality, while C(s) remains divergent as in the unconstrained system. We are able to explain these observed constrained phenomena on the basis of the Fisher renormalization mechanism generalized to include a subleading relevant thermal scaling field. In this context, we find that, under the constraint, the leading thermal exponent y(t1) is renormalized to 2- y(t1) , while the subleading exponent y(t2) remains unchanged.