Third-order magnetic susceptibility of the frustrated square-lattice antiferromagnet

TL;DR

This paper investigates the temperature-dependent third-order magnetic susceptibility of the frustrated square-lattice J1-J2 Heisenberg model using exact diagonalization, aiming to clarify exchange interactions across various phases.

Contribution

It introduces a finite-temperature Lanczos approach to analyze the third-order susceptibility, providing new insights into exchange constants in frustrated magnetic systems.

Findings

Identified temperature dependence patterns of third-order susceptibility.

Resolved ambiguity in exchange constants across different phases.

Mapped susceptibility behavior over the entire frustration angle range.

Abstract

We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites utilizing the finite-temperature Lanczos method. In particular, we focus on the temperature dependence of the third-order magnetic susceptibility as a method to resolve the ambiguity of exchange constants. We discuss the entire range of the frustration angle $\phi=\tan^{-1}(J_{2}/J_{1})$ parameterizing the different possible phases of the model, including the large region in the phase diagram with at least one ferromagnetic exchange constant.