Fixed-phase approximation, Monte Carlo

The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115 497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval. 

SO far in detail. From the point of view of pure theory, or of Monte Carlo simulations, it is practical to regard temperature T, bond probability p, and monomer concentration (j> as three independent variables and to study phase transition surfaces in this T - p - space. (The special plane p = 1 corresponds to Fig. 5 above, the limit T = < to Fig. 6.) At a fixed temperature T above the critical consolute temperature Tc, i.e. in the one-phase region one has curves similar to the T = > limit of Fig. 6 only the end point at p = 1 is shifted slightly to lower concentrations

quantitative results for these percolation line in the simple cubic lattice on the basis of Monte Carlo simulations. (At temperatures appreciably below the phase separation temperature T the system is separated into one phase with very few monomers where even for p = 1 no gelation is possible, and another phase with very few solvent molecules where the system is approximated well by random-bond percolation, 0 = 1.)... 

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