Phase Transition of Ferromagnetic Ising Spins on Husimi Lattice of Variable Unit Ensemble

Abstract

The Husimi recursive lattice is extended to a hybrid ensemble of variable unit cells. This enables the Husimi lattice to be more versatile in describing complex systems, including those with an odd coordination number or a cross-dimensional feature. The independence of units in the recursive lattice also makes it possible to use a randomly arranged unit ensemble to explore the stochasticity and thermal fluctuation following exact thermodynamic calculations. A simple recursive configuration with square and cube units is constructed and calculated by modeling ferromagnetic Ising spins on the lattice. Both fixed and randomly arranged hybrid lattices are preliminarily investigated. The spontaneous magnetization transition and corresponding thermodynamics are shown and compared with the Bethe lattice and fractional-branched Husimi lattice with the analog of coordination numbers.