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

Abstract

The multi-branched Husimi recursive lattice has been extended to a virtual structure with fractional numbers of branches joined on one site. Although the lattice is undrawable in real space, the concept is consistent with regular Husimi lattice. The Ising spins of antiferromagnetic interaction on such a sets of lattices were calculated to check the critical temperatures (T c ) and ideal glass transition temperatures (T k ) variation with fractional branch numbers. Besides the similar results of two solutions representing the stable state (crystal) and metastable state (supercooled liquid) and indicating the phase transition temperatures, the phase transitions show a well-defined shift with branch number variation. Therefore the fractional branch number as a parameter can be used as an adjusting tool in constructing a recursive lattice model to describe real systems.

Thermodynamic Comparison and the Ideal Glass Transition of Antiferromagnetic Ising Model on Multi-branched Husimi and Cubic Recursive Lattice with the Identical Coordination Number

“…The CRL calculation is similar to the method introduced in the previous section and can be found in Ref. [19]. Here we briefly give the scheme of the CRL calculation.…”

“…For several decades it has been extended to be in various forms constructed from different kinds of units, such as triangle, hexagon, tetrahedron, cube, and so on [16][17][18]. In this paper, we construct a multi-branched square HL [19] and compare its behavior with a Husimi cubic recursive lattice (CRL), both of which are designed to approximate the regular 3-D cubic lattice whose coordination number q is 6. We will specifically study an antiferromagnetic Ising model on them and solve it exactly to investigate various equilibrium and time-independent metastable phases.…”

Ising spins on randomly multi-branched Husimi square lattice: Thermodynamics and phase transition in cross-dimensional range

“…The thermodynamic calculations again follows the same principle detailed in Ref. [13,24], while a slight modification is necessary to fit the random conformation case. Herein we firstly review the general method to calculate the free energy on a homogeneous B-branched Husimi lattice.…”

Theoretical exploration on the magnetic properties of ferromagnetic metallic glass: An Ising model on random recursive lattice

“…Then this model can be exactly solved by the recursive relations between the PF and PPFs on successive levels to obtain the probability of spins' state at particular temperature, and the magnetization and thermodynamics can be derived from the probability. For the calculation details please refer to previous works on the Ising model on Husimi lattice [25,[28][29][30] and the supplemental materials.…”