1,721,346 research outputs found
Thermodynamic properties of a full-replica-symmetry-breaking Ising spin glass on lattice gas: The random Blume-Emery-Griffiths-Capel model
No full textAn extensive study of the mean-field static solution of the random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable replica-symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a full-replica-symmetry-breaking spin-glass phase. The nature of the transition can be either of the second order (such as in the Sherrington-Kirkpatrick model) or, at temperatures below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case, coexistence of phases takes place. The thermodynamics is worked out in the full-replica-symmetry-breaking scheme, and the related Parisi equations are solved using a pseudospectral method down to zero temperature
Long-range random-field Ising model: Phase transition threshold and equivalence of short and long ranges
No full textReply to Comment on ``Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition''
No full textIn his Comment, Krakoviack Phys. Rev. B 76 136401 (2007)] finds that the phase behavior of the s+p spin-glass model is different from that proposed by Crisanti and Leuzzi Phys. Rev. B 73 014412 (2006) if s and p are larger than 2 and are separated well enough. He proposes a trial picture, based on a one step replica symmetry breaking solution, displaying a mode-coupling-like glass-to-glass transition line ending in an A3 singularity. However, actually, the physics of these systems changes when p−s is large, the instability of which the one step replica symmetry breaking glassy phase suffers turns out to be so wide ranging that the whole scenario proposed by Krakoviack must be seriously reconsidered
The 3-SAT problem with large number of clauses in the ∞-replica symmetry breaking scheme
No full textIn this paper we analyse the structure of the UNSAT-phase of the over-constrained 3-SAT model by studying the low temperature phase of the associated disordered spin model. We derived the full replica symmetry breaking (RSB) equations for a general class of disordered spin models which includes the Sherrington–Kirkpatrick (SK) model, the Ising p-spin model as well as the over-constrained 3-SAT model as particular cases. We have numerically solved the ∞-RSB equations using a pseudo-spectral code down to and including zero temperature. We find that the UNSAT-phase of the over-constrained 3-SAT is of the ∞-RSB kind: in order to get a stable solution the replica symmetry has to be broken in a continuous way, similarly to the SK model in an external magnetic field
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