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

Hidetoshi Nishimori

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Phys. Rev. E 114, 044127 – Published 19 October, 2026

DOI: https://doi.org/10.1103/1xrx-rsxn

Abstract

Reentrant transitions and temperature chaos are two unusual properties of spin glasses. We recently established a general 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.

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Phys. Rev. E 114, 044127– Published 19 October, 2026
  • Received 29 August 2026
  • Accepted 5 October 2026
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