相关论文: Complexity of the Sherrington-Kirkpatrick Model in…

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz…

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of…

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…

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…

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…

Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…

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…

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…

In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interactions are allowed between spins lying in adjacent layers and…

This paper characterizes the annealed complexity of bipartite spherical spin glasses, both pure and mixed. This means we give exact variational formulas for the asymptotics of the expected numbers of critical points and of local minima.…

We prove that the topological complexity of every symplectically atoroidal manifold is equal to twice its dimension. This is the analogue for topological complexity of a result of Rudyak and Oprea, who showed that the…

We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the…

We compute the Bray and Moore (BM) TAP Complexity for the Sherrington-Kirkpatrick model through the cavity method, showing that some essential modifications are needed with respect to the standard formulation of the method. This allows to…

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…

We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of…

In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…

We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models…

The concept of statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allows us to understand this driven…

The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point…