相关论文: Quenched Computation of the Complexity of the Sher…

By using the BRST supersymmetry we compute the quenched complexity of the TAP states in the SK model. We prove that the BRST complexity is equal to the Legendre transform of the static free energy with respect to the largest replica…

The Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry is a powerful tool for the calculation of the complexity of metastable states in glassy systems, and it is particularly useful to uncover the relationships between complexity and standard…

A careful critical analysis of the complexity, at the annealed level, of the Sherrington-Kirkpatrick model has been performed. The complexity functional is proved to be always invariant under the Becchi-Rouet-Stora-Tyutin supersymmetry,…

In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap.…

We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the…

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

We analyze a two-body nonhermitian two-site Sachdev-Ye-Kitaev model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of phase transitions…

Based on the modified Thouless-Anderson-Palmer equations a detailed numerical investigation for the complexity of the Sherrington-Kirkpatrick spin glass is worked out. The data suggest a scaling law which leads to a vanishing of the…

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington-Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of…

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from…

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…

We give a proof of the replica symmetric formula for the free energy of the Sherrington-Kirkpatrick model in high temperature which is based on the TAP formula. This is achieved by showing that the conditional annealed free energy equals…

The authors of [Ann. Henri Poincar\'{e} 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica…

The Sherrington-Kirkpatrick (SK) model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches,…

We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rules by computing the partially quenched chiral condensate to…

We consider the Sherrington-Kirkpatrick model and we prove that the thermodynamic limit of the quenched free energy per site is strictly greater than the corresponding replica symmetric approximation, for all values of the temperature and…

In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…

We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into the asymptotic energy limit. Our approach involves integro-differential equations, incorporating the Crisanti-Horner-Sommers-Cugliandolo-Kurchan…

The supersymmetry self-consistent approximation for the model of non-equilibrium thermodynamic system with quenched disorder is derived from the dynamical action calculated by means of generalized second Legendre transformation. The…

In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…