Exact solution of a RNA-like polymer model on the Husimi lattice

Abstract

We investigate a two-tolerant polymer model on the square Husimi lattice, which aims at describing the properties of RNA-like macromolecules. We solve the model in a numerically exact way, working out the grand-canonical phase diagram, both with and without taking into account the stacking effect. Besides a nonpolymerized phase, we observe two different polymerized phases characterized by a lower or higher density of doubly visited lattice bonds. The system exhibits three qualitatively different regimes, as a function of the monomer chemical potential. Below some T1 temperature and above some T2 temperature, the transition to the nonpolymerized phase is continuous, whereas, in the (T1,T2) temperature range, the transition is first order. In the dilute-solution limit, the high temperature regime corresponds to a swollen ("coil") state, the intermediate regime to a moderately collapsed ("molten") state, with a small fraction of paired segments, and the low temperature regime to an almost fully paired ("native") state. The molten state ends in a tricritical (Theta-like) transition at high temperature and in a critical end point at low temperature. Upon increasing the stacking energy parameter, the temperature range of the molten state turns out to be progressively reduced but never completely removed.

The first order phase transitions in the multisite spin-1/2 model on a pure Husimi lattice

“…During last few decades, a lot of classical Ising and Ising-like models have been investigated on various pure Husimi trees and lattices [1][2][3] (see the next section for their exact definition) which play important role in describing many interesting physical systems such as amorphous solids [4], spin liquids [5], the Ising spin glasses [6][7][8][9], various polymer models [10][11][12][13][14][15], abelian sandpiles [16,17], lattice gases [18], and 3 He systems [19]. At the same time, various models on pure Husimi trees and lattices are especially useful for investigation of physical systems in which multisite interactions play important role, i.e., for investigating such systems as, e.g., binary alloys, rare gases, lipid bilayers [20], or spin glasses [21].…”

Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices

“…The method is widely used to investigate exact solution of spin models on hierarchical lattices, which are good approximations for real ones (the so called Bethe-Peierls approximation) [11][12][13][14][15][16]. This technique can also be applied to the generalized Bethe (Husimi) lattice, to describe properties of frustrated systems with multisite interactions, and RNA-like polymers [17][18][19]. The multisite interaction Ising and Q-state Potts models are of particular interest: the first one is efficient in the analysis of magnetic properties of solid 3 He [20,21], while Potts model, apart of being strongly related to problems in magnetism [22][23][24], falls in the same universality class as gelation processes in branched polymers [25,26]; note that the model is well-defined for non-integer values of Q (as pointed out in [27]).…”

Thermodynamic Transitions of Antiferromagnetic Ising Model on the Fractional Multi-branched Husimi Recursive Lattice

“…The recursive lattice is believed to be a reliable approximation of regular lattices because of the same coordination numbers. In a recursive lattice the particles fixed on sites have the same interaction environment as in the regular lattices, while the fractal structure avoids the sharing of interactions on neighbor units and consequently provides the advantage of the exact calculation 3,4 Among the works on Husimi lattice, the thermodynamics of Ising model on Husimi is a vigorously interest-drawing subject [5][6][7][8][9][10][11][12][13][14] . Previous works on exact calculation of Ising model on Husimi successfully presented comparable results with other techniques, e.g.…”