We study an associating lattice gas (ALG) using Monte Carlo simulation and solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules. We focus on the transition between the high-density liquid (HDL) phase and the isotropic gas phase in the limit of full occupancy ($μ\to \infty$). Simulation results show a continuous phase transition at $τ_c=k_BT_c/γ=0.4763(1)$ (where $-γ$ is the bond energy) between the low-temperature HDL phase, with a non-vanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice results furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures ($τ_c=0.51403$ and $0.51207$ for trees built with triangles and hexagons, respectively) are slightly higher than the one found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous gas-HDL line for finite $μ$, three possible scenarios arise. The first is that in the limit $μ\to \infty$ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.
Theory of associating polymers with annealed and quenched sticker disorder: Mean-field solution and phase behavior
Scuola Internazionale Superiore di Studi Avanzati (SISSA)（高等师范研究所）；Università Ca’ Foscari Venezia（威尼斯大学）；European Centre for Living Technology (ECLT)（生命技术欧洲中心）；University of Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
