Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model

TL;DR

This paper investigates the finite-temperature Ising phase transition in the two-dimensional quantum $J_1-J_2$ Heisenberg antiferromagnet on a square lattice, revealing its persistence across different spin values and its relation to experimental compounds.

Contribution

It demonstrates the existence of a finite-temperature Ising transition in the collinear phase for all spin values using the self-consistent harmonic approximation.

Findings

Finite-temperature Ising transition persists for all spins in the collinear phase.

The transition occurs when the $J_2/J_1$ ratio exceeds a critical value.

Results align with experimental observations in Li$_2$VOSiO$_4$ and similar materials.

Abstract

We study the thermodynamics of the spin-$S$ two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor couplings in its collinear phase ($J_2/J_1>0.5$), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio $J_2/J_1$ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li$_2$VOSiO$_4$ and related compounds.