Weak universal critical behaviour of the mixed spin-(1/2, S) Ising model on the union jack (centered square) lattice: integer versus half-odd-integer spin-S case

TL;DR

This study explores the complex critical phenomena of the mixed spin-(1/2, S) Ising model on a union jack lattice, revealing weak universal critical behaviour and differences between integer and half-odd-integer spins.

Contribution

It establishes a mapping between the mixed spin model and the eight-vertex model, uncovering novel variations in critical exponents for different spin types.

Findings

Reentrant phase transitions observed.

Weak universal critical behaviour identified.

Critical exponents vary along bicritical lines, differing for integer and half-odd-integer spins.

Abstract

The mixed spin-(1/2, S) Ising model on the union jack (centered square) lattice is investigated by establishing the mapping relationship with its corresponding eight-vertex model. An interplay between the nearest-neighbour interaction, the competing next-nearest-neighbour interaction and the single-ion anisotropy gives rise to a rather complex critical behaviour displayed in the reentrant phase transitions, the weak universal critical behaviour, as well as, a presence of first- and second-order phase transitions. The most interesting finding to emerge from the present study relates to a variation of the weak-universal critical exponents along the line of bicritical points, which is being twice as large for the mixed spin-(1/2, S) systems with the integer spin-S atoms as for the ones with the half-odd-integer spin-S atoms.