Numerical study of a lattice-gas model for micellar binary solutions

Two nonperturbative methods such as transfer-matrix finite-size scaling and Monte Carlo simulations are used to investigate the multicritical behavior of a lattice-gas model proposed by Shnidmas and Zia [J. Stat. Phys 50, 839 (1988)] for studying the micellar binary solutions of water and amphiphile. The phase diagrams are obtained in both the magnetic field-temperature JH,TI and amphiphile density temperature (rho(s),T) for different values of competing interactions (K-0 and K-1) and in the presence of the attraction interaction intermicellar parameter (J). Our nonperturbative results are compared with previous mean-held ones. Both methods confirm the absence of the rarefied micelle at high temperature as found previously by mean-field calculations. Also our phase diagrams present transitions of first- and second-order transitions linked by tricritical and multicritical points of higher order. Finally, with the use of finite-size-scaling ideas, the critical exponents have been calculated. Our results show that this model has a nonuniversal behavior that belongs to the XY model with cubic anisotropy for a certain range of interactions parameters and a universal behavior that belongs to the d = 2 Ising model.