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 c ompeting interactions (K-0 and K-1) and in the presence of the attraction i nteraction intermicellar parameter (J). Our nonperturbative results are com pared with previous mean-held ones. Both methods confirm the absence of the rarefied micelle at high temperature as found previously by mean-field cal culations. 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 ex ponents have been calculated. Our results show that this model has a nonuni versal behavior that belongs to the XY model with cubic anisotropy for a ce rtain range of interactions parameters and a universal behavior that belong s to the d = 2 Ising model.