Universally non-diverging Grüneisen parameter at critical points

Abstract

According to Boltzmann-Gibbs (BG) statistical mechanics, the thermodynamic response, such as the isothermal susceptibility, at critical points (CPs) presents a divergent-like behavior. An appropriate parameter to probe both classical and quantum CPs is the so-called Grüneisen ratio $\Gamma$. Motivated by the results reported in Phys. Rev. B $\text{108}$, L140403 (2023), we extend the quantum version of $\Gamma$ to the non-additive $q$-entropy $S_q$. Our findings indicate that using $S_q$ at the unique value of $q$ restoring the extensivity of the entropy, $\Gamma$ is universally non-diverging at CPs. We unprecedentedly introduce $\Gamma$ in terms of $S_q$, being BG recovered for $q\to 1$. We thus solve a long-standing problem related to the $\text{illusory}$ diverging susceptibilities at CPs.

5 pages, 3 figs, comments are welcome