Thermodynamic geometry of a kagome Ising model in a magnetic field

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 $\mathrm{\mid }\beta -{\beta }_c{\mathrm{\mid }}^{\alpha -2}$ 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 $\mathrm{\mid }\beta -{\beta }_c{\mathrm{\mid }}^{\alpha -1}$.