Strong- and weak-universal critical behaviour of a mixed-spin Ising model with triplet interactions on the Union Jack (centered square) lattice

TL;DR

This paper exactly solves a mixed-spin Ising model with triplet interactions on a Union Jack lattice, revealing both strong- and weak-universal critical behaviors depending on interaction anisotropy and spin type.

Contribution

It establishes a rigorous mapping of the model to the eight-vertex model and analyzes the influence of anisotropy and single-ion anisotropy on critical phenomena.

Findings

Model exhibits strong-universal critical behavior with constant exponents in isotropic and certain anisotropic cases.

Anisotropic models with two different triplet interactions show weak-universal behavior with variable exponents.

Critical exponents vary significantly between integer and half-odd-integer spin cases.

Abstract

The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.