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.

Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations / T., Castellani; F., Krzakala; RICCI TERSENGHI, Federico. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - 47:1(2005), pp. 99-108. [10.1140/epjb/e2005-00293-1]

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

RICCI TERSENGHI, Federico
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.
2005
01 Pubblicazione su rivista::01a Articolo in rivista
Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations / T., Castellani; F., Krzakala; RICCI TERSENGHI, Federico. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - 47:1(2005), pp. 99-108. [10.1140/epjb/e2005-00293-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/127386
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