Thermodynamic geometry of a kagome Ising model in a magnetic field

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 $|β-β_{c}|^{α-2}$ for $α> 0$ where $β$ is the inverse temperature and $α$ is the critical exponent of specific heat. In the model considered here in which $α$ is zero, we found that $R$ behaves as $|β-β_{c}|^{α-1}$.