A Husimi rhombus lattice with random angles to present the configurational stochasticity in exact thermodynamic calculation

Abstract

Abstract The square unit in Husimi lattice is generalized to be rhombus with random angles. The independence feature of unit cells in recursive lattice makes the random conformation possible, which is unfeasible in conventional lattices. Since the randomness of conformations in real system is naturally introduced into the model, this new lattice can describe the off-crystal metastable states without artificial randomness. With reasonable simplification, a coefficient A ( θ ) is formulated to present the effect of angle in the rhombus unit. A “visit and count” recursive calculation is developed to numerically approach the thermodynamics. The critical temperature T c of spontaneous magnetization is lowered with the presence of angle randomness, implying a less stable system. Besides consistent results to the regular lattice, the random-angled model features a distribution of solutions and thermal fluctuation with exact calculation. The Kauzmann paradox and ideal glass transition due to the off-crystal metastable portion are identified by the appearance of negative entropy. The effects of energy parameters on thermodynamics and the ground states are investigated.