Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes

Abstract

We study binary mixtures of hard particles, which exclude up to their kth nearest neighbors (kNN) on the simple cubic lattice and have activities z k . In the first model analyzed, point particles (0NN) are mixed with 1NN ones. The grand-canonical solution of this model on a Husimi lattice built with cubes unveils a phase diagram with a fluid and a solid phase separated by a continuous and a discontinuous transition line which meet at a tricritical point. A density anomaly, characterized by minima in isobaric curves of the total density of particles against z0 (or z1), is also observed in this system. Overall, this scenario is identical to the one previously found for this model when defined on the square lattice. The second model investigated consists of the mixture of 1NN particles with 2NN ones. In this case, a very rich phase behavior is found in its Husimi lattice solution, with two solid phases -one associated with the ordering of 1NN particles (S1) and the other with the ordering of 2NN ones (S2) -, beyond the fluid (F ) phase. While the transitions between F -S2 and S1-S2 phases are always discontinuous, the F -S1 transition is continuous (discontinuous) for small (large) z2. The critical and coexistence F -S1 lines meet at a tricritical point. Moreover, the coexistence F -S1, F -S2 and S1-S2 lines meet at a triple point. Density anomalies are absent in this case. * nathan.rodrigues@ufv.br † tiago@ufv.br

Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor

“…The power of the flat histogram method is amplified when applied to densities of states which depend on more than one variable. A viable example is the binary gas, the simplest of which is a mixture of 1-NN and 0-NN particles which shows a nontrivial phase diagram with a tricritical point [81][82][83][84][85][86]. Similarly, multidimensional densities of states appear in HCLG with additional attractive interactions [38,39,[87][88][89].…”

Rejection-free cluster Wang-Landau algorithm for hard-core lattice gases

“…Flat histogram methods have a significant advantage in being able to access the full phase space in one sweep of the configuration space. The simplest model to study will be the mixture of 1-NN and 0-NN particles which shows a nontrivial phase diagram with a tricritical point [77][78][79][80][81][82][83]. Estimating the critical parameters for the model from the flat histogram method would be a starting point.…”