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.