Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagome lattice

TL;DR

This paper analyzes a mixed-spin Ising model on the extended Kagome lattice, revealing both universal and non-universal critical behaviors through exact solutions and mappings to the eight-vertex model.

Contribution

It establishes an exact solution for the model via mapping to the eight-vertex model and identifies conditions leading to universal and non-universal critical exponents.

Findings

Critical points follow the standard Ising universality class.

Existence of a coexistence surface with exactly solvable symmetric eight-vertex model.

Presence of bicritical points with non-universal, interaction-dependent critical exponents.

Abstract

The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom\'e lattice is solved by establishing a mapping correspondence with the eight-vertex model. Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the model becomes exactly soluble as a free-fermion eight-vertex model. Under this restriction, the critical points are characterized by critical exponents from the standard Ising universality class. In a certain subspace of interaction parameters that corresponds to a coexistence surface between two ordered phases, the model becomes exactly soluble as a symmetric zero-field eight-vertex model. This surface is bounded by a line of bicritical points that have non-universal interaction-dependent critical exponents.