Thermodynamics of the $q$-deformed Kittel--Shore model

TL;DR

This paper investigates how $q$-deformation of the Kittel--Shore model influences thermodynamic properties like specific heat and phase transitions in spin-$1/2$ systems, revealing shifts to higher temperatures and modified phase behavior.

Contribution

It provides the first detailed analysis of thermodynamic effects resulting from $q$-deformation in the Kittel--Shore model, connecting quantum group symmetry to physical properties.

Findings

Deformation shifts thermodynamic behaviors to higher temperatures.

Altered phase transition characteristics due to $q$-deformation.

Potential for describing non-uniform spin systems.

Abstract

The Kittel--Shore Hamiltonian characterizes $N$ spins with identical long-range interactions, and the $\mathfrak{su}(2)$ coalgebra has been proven to be a symmetry of this model, which can be exactly solved. By using quantum groups and, in particular, $\mathfrak{su}_{q}(2)$, this Hamiltonian was deformed. In this work, we study the thermodynamic properties of this deformed model for spin-$1/2$ particles. In particular, we discuss how this deformation affects the specific heat, magnetic susceptibility, magnetisation, and phase transitions as a function of the parameter $q$ of the deformation and compare them with those of the undeformed model. Deformation was found to shift the thermodynamic behaviours to higher temperatures and alter the phase transitions. The potential applications of this $q$-deformed model for describing few-spin quantum systems with non-identical couplings are discussed.