Reentrance and temperature chaos in the $p$-spin Ising spin glass

Abstract

Reentrant transitions and temperature chaos are two unusual properties of spin glasses and had long been considered physically unrelated. We recently established a logical relation between these two phenomena [Phys. Rev. E 112, 044140 (2025)]. In the present paper, we provide an explicit example of this logical relation in the fully connected Ising $p$-spin glass with a ferromagnetic bias. By expanding the free energy around the triple point, we show analytically that the ferromagnetic--spin glass boundary is reentrant in the vicinity of the triple point throughout the examined range of finite $p>2$. It then follows from the above logical relation that there exists at least one pair of distinct temperatures in the spin glass phase for which the overlap of spin configurations vanishes. This is a necessary condition for temperature chaos, but it would be quite unusual for the overlap to vanish only for selected temperature pairs but not for others within a single spin glass phase. These results therefore strongly suggest the existence of temperature chaos in the sense that the overlaps of spin configurations vanish for all temperature pairs throughout the spin glass phase. Independent evidence for this behavior is provided by a two-temperature replica calculation.