Nonperturbative thermodynamic extrinsic curvature of the anyon gas

TL;DR

This paper introduces a nonperturbative thermodynamic extrinsic curvature for an anyon gas and analyzes its critical behavior in various models, revealing new fixed points and distinct scaling laws near critical points.

Contribution

It presents the first nonperturbative thermodynamic extrinsic curvature for an anyon gas and explores its critical behavior in different models, uncovering new fixed points and scaling laws.

Findings

Identifies new fixed points in the thermodynamics of anyon gases.

Shows the extrinsic curvature scales with critical exponents in specific models.

Reveals different scaling behaviors of extrinsic curvature depending on the sign of the critical exponent.

Abstract

Thermodynamic extrinsic curvature is a new mathematical tool in thermodynamic geometry. By using the thermodynamic extrinsic curvature, one may obtain a more complete geometric representation of the critical phenomena and thermodynamics. We introduce nonperturbative thermodynamic extrinsic curvature of an ideal two dimensional gas of anyons. Using extrinsic curvature, we find new fixed points in nonperturbative thermodynamics of the anyon gas that particles behave as semions. Here, we investigate the critical behavior of thermodynamic extrinsic curvature of two-dimensional Kagome Ising model near the critical point $ \beta_{c} =({{k_{B} T_{c}}})^{-1}$ in a constant magnetic field and show that it behaves as $ \left| {\beta- \beta_{c} } \right|^{\alpha} $ with $ \alpha=0 $, where $ \alpha $ denotes the critical exponent of the specific heat. Then, we consider the three dimensional spherical model and show that the scaling behavior is $ \left| {\beta- \beta_{c} } \right|^{\alpha} $ , where $ \alpha =-1 $. Finally, using a general argument, we show that extrinsic curvature $ K $ have two different scaling behaviors for positive and negative $ \alpha $. For $\alpha> 0$, our results indicate that $ K \sim \left|{\beta- \beta_{c} } \right|^{{\frac{1}{2}} (\alpha-2)} $. However, for $ \alpha <0$, we found a different scaling behavior, where $ K\sim \left| {\beta- \beta_{c} } \right|^{\alpha} $.