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
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.
PACS: 75.50.Lk – Spin glasses and other random magnets / 75.40.Cx – Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.) / 64.60.Fr – Equilibrium properties near critical points, critical exponents
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
