Statistical recovery of the classical spin Hamiltonian

TL;DR

This paper introduces a straightforward method to infer classical spin Hamiltonian parameters from correlation functions and specific heat data, demonstrated on various models and applicable to experimental magnetization images.

Contribution

The paper presents a novel, simple procedure for extracting interaction parameters of classical spin Hamiltonians from correlation and heat capacity data.

Findings

Successfully applied to 1D and 2D Ising models

Extended to 2D Heisenberg model with Dzyaloshinkii-Moriya interaction

Provides a practical recipe for experimental data analysis

Abstract

We propose a simple procedure by which the interaction parameters of the classical spin Hamiltonian can be determined from the knowledge of four-point correlation functions and specific heat. The proposal is demonstrated by using the correlation and specific heat data generated by Monte Carlo method on one- and two-dimensional Ising-like models, and on the two-dimensional Heisenberg model with Dzyaloshinkii-Moriya interaction. A recipe for applying our scheme to experimental images of magnetization such as those made by magnetic force microscopy is outlined.