Rényi complexity in mean-field disordered systems
Nina Javerzat (LiPhy Grenoble)
Configurational entropy, or complexity, quantifies the number of metastable states within (free) energy landscapes, and plays therefore a critical role in characterizing disordered systems such as glasses. Yet, its measurement often requires significant computational resources. Recently, Rényi entropy, a one-parameter generalization of the Shannon entropy, has gained attention across various fields of physics due to its simpler functional form, making it more practical for measurements. I will explain that the Rényi complexity corresponds, in disordered models, to the difference of the free energy of a cloned system and the original one (a generalized Franz-Parisi potential). I will give a pedagogical overview of the case of the mean-field p-spin spherical model, where the computation of Rényi complexities can be performed analytically via the replica trick. Our results show that for models having one-step replica symmetry breaking (RSB), the Rényi complexities vanish at the Kauzmann temperature Tk, suggesting that they are a useful observable for estimating Tk in practical applications. Moreover, we show that RSB solutions are required even in the liquid phase, where interesting relationships are found between Rényi complexities and the annealed Franz-Parisi potential.
Based on arXiv:2411.19817