2 papers
math.PR2026
A Sharp Universality Dichotomy for the Free Energy of Spherical Spin Glasses
Taegyun Kim
We study the free energy for pure and mixed spherical -spin models with i.i.d.\ disorder. In the mixed case, each -interaction layer is assumed either to have regularly varyi…
math.PR2025
Heavy-Tailed Mixed p-Spin Spherical Model: Breakdown of Ultrametricity and Failure of the Parisi Formula
Taegyun Kim
We prove that the two cornerstones of mean-field spin glass theory -- the Parisi variational formula and the ultrametric organization of pure states -- break down under heavy-taile…