Magnetoelastic signatures of thermal and quantum phase transitions in a deformable Ising chain under a longitudinal and transverse magnetic field

TL;DR

This paper studies a deformable Ising chain under magnetic fields, revealing magnetoelastic effects and phase transitions, including discontinuous thermal and continuous quantum transitions, with implications for elastic and magnetic properties.

Contribution

It provides an exact theoretical framework for magnetoelastic signatures of phase transitions in a deformable Ising chain under different magnetic fields.

Findings

Discontinuous thermal phase transitions with hysteresis in longitudinal field.

Continuous quantum phase transition with diverging susceptibility in transverse field.

Elastic softening and sound attenuation near phase transitions.

Abstract

We investigate a deformable spin-1/2 Ising chain subjected to either a longitudinal or a transverse magnetic field, which incorporates a magnetoelastic coupling linearly dependent on a lattice distortion parameter. Within the harmonic and static adiabatic approximations, the variational Gibbs free energy is evaluated exactly using transfer-matrix and Jordan-Wigner fermionization techniques and then minimized self-consistently with respect to the lattice distortion parameter. This approach enables a unified description of magnetic and elastic properties including the magnetization, magnetic susceptibility, lattice distortion, inverse compressibility, and relative change in the sound velocity. In a longitudinal magnetic field, the deformable Ising chain displays a line of discontinuous thermal phase transitions terminating at a critical point. The discontinuous transitions are accompanied by metastable states, which give rise to a hysteresis loop at low temperatures. In contrast, the deformable Ising chain in a transverse field undergoes exclusively a continuous quantum phase transition at zero temperature with no indication of thermal phase transitions. The magnetic susceptibility and inverse compressibility exhibit cusp- and dip-like anomalies at discontinuous phase transitions, while a diverging susceptibility and vanishing inverse compressibility characterize the continuous phase transitions. An elastic softening of the deformable chain near thermal and quantum phase transitions manifest itself also through a significant sound attenuation.