Thermodynamic geometry of a kagome Ising model in a magnetic field

TL;DR

This paper calculates the thermodynamic curvature of a kagome lattice Ising model under magnetic field, revealing critical behavior and scaling relations near phase transitions.

Contribution

It derives the thermodynamic curvature for the kagome Ising model in a magnetic field, highlighting its singularity at critical points and scaling behavior for zero field.

Findings

Curvature has a singularity at the critical point.

In zero field, curvature scales as |eta - eta_c|^{ ext{α}-1}.

Behavior consistent with critical scaling theory.

Abstract

We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive thermodynamic curvature and its components near the criticality. According to standard scaling, scalar curvature $R$ behaves as $|\beta-\beta_{c}|^{\alpha-2}$ for $\alpha > 0$ where $\beta$ is the inverse temperature and $\alpha$ is the critical exponent of specific heat. In the model considered here in which $\alpha$ is zero, we found that $R$ behaves as $|\beta-\beta_{c}|^{\alpha-1}$.