Eur. Phys. J. B 29, 425-435 (2002)
https://doi.org/10.1140/epjb/e2002-00274-x

Ultrametricity between states at different temperatures in spin-glasses

Dipartimento di Scienze Fisiche, Università “Federico II”, Complesso Monte S. Angelo, 80126 Napoli, Italy

Corresponding author: ^a tommaso.rizzo@inwind.it

Received: 18 March 2002
Revised: 14 June 2002
Published online: 1 October 2002

Abstract

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-p-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model.