The 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.

arXiv comment11 pages, 6 figures

References in corpus (2)

• Configurational Entropy and its Crisis in Metastable States: Ideal Glass Transition in a Dimer Model as a Paragidm of a Molecular Glass
• Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

Cited by in corpus (4)

• Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number
• Theoretical Exploration on the Magnetic Properties of Ferromagnetic Metallic Glass: An Ising Model on Random Recursive Lattice
• Ising Spins on Randomly Multi-Branched Husimi Square Lattice: Thermodynamics and Phase Transition in Cross-dimensional Range
• Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices