Order-disorder transition in a two-dimensional associating lattice gas

Abstract

We study an associating lattice gas (ALG) using Monte Carlo simulation on the triangular lattice and semianalytical 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, mimicking the formation of hydrogen bonds. We focus on the transition between the high-density liquid (HDL) phase and the isotropic gas phase in the limit of full occupancy, corresponding to chemical potential µ → ∞, which has not yet been studied systematically. Simulation results show a continuous phase transition at τ c = k B T 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 → ∞ 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.Following the ideas of Bell and Lavis, Henriques and Barbosa introduced a two-dimensional (2D) associating arXiv:1903.08306v1 [cond-mat.stat-mech]

Phase diagram and critical properties of a two-dimensional associating lattice gas

“…We study the symmetric version of the Henriques and Barbosa (H&B) 21 associating lattice gas (ALG) model, investigated in Refs. 22,34,35,41 . The model is defined on the triangular lattice (coordination number z = 6), where each site i can be either empty (σ i = 0) or occupied by a single molecule (σ i = 1).…”

“…Following Ref. 41 , we may conveniently define an orientational variable, η i , pointing along one of the nonbonding directions of the molecule at site i. In this fashion, it is simply given by the generators of the triangular lattice, êk with k = 1, 2 and 3, which are also depicted in Fig.…”

“…We remark that in Ref. 41 the temperature (called τ there) was defined in units of γ, so that τ = T /2. As already discussed in the Introduction [Sec.…”

“…More recently, this symmetric H&B model was investigated in the limit of full occupancy (corresponding to a chemical potential µ → ∞) using MC simulations and semi-analytical solutions on Husimi lattices 41 . The simulations yielded a continuous transition between the HDL and the DF phase at a (reduced) temperature Tc = 0.9525 (5), with critical exponents and Binder cumulant in good agreement with those of the three-state Potts model in 2D 42 .…”

“…However, in contrast with the mean-field result 34 shown in this figure, we find that the transition between the DF and HDL phases is always continuous and the critical DF-HDL line ends at a critical-end-point, where it meets the DF-LDL and LDL-HDL coexistence lines. The critical properties of the continuous transition line -an interesting problem scarcely tackled in the literature of lattice models for water (see 41 for a discussion) -are also investigated and an intriguing behavior is found, with some quantities presenting a close agreement with the threestate Potts class, while others have a large deviation from it.…”