Eur. Phys. J. B 47, 99-108 (2005)
https://doi.org/10.1140/epjb/e2005-00293-1

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

¹ Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, Roma 00185, Italy
² Laboratoire P.C.T., UMR CNRS 7083, ESPCI, 10 rue Vauquelin, 75005 Paris, France

Received: 8 March 2004
Revised: 11 May 2005
Published online: 21 September 2005

Abstract

We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find three phases: a replica-symmetric (RS) ferromagnetic one, a magnetized spin glass one (the so-called mixed phase), and an unmagnetized spin glass one. We are able to give analytic expressions for the critical point where the RS phase becomes unstable with respect to 1RSB solutions: we also clarify the mechanism inducing such a phase transition. Finally we compare our analytical results with the outcomes of a numerical algorithm especially designed for finding ground states in an efficient way, stressing weak points in the use of such numerical tools for discovering RSB effects. Some of the analytical results are given for generic connectivity.