Related papers: A remark on the spherical bipartite spin glass

We argue that the lower bound to the barrier energy to flip an up/down spin domain embedded in a down/up spin environment for Ising spin glass is independent of the size of the system. The argument shows the existence of at least one…

We introduce the concept of Random Multi-Overlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for non-diluted models. As a result, we prove the generalized bound and variational principle for the free…

Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…

We study the replica free energy surface for a spin glass model near the glassy temperature. In this model the simplicity of the equilibrium solution hides non trivial metastable saddle points. By means of the stability analysis performed…

We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\'e inequality. This complements…

In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass…

The limit free energy of spin-glass models with convex interactions can be represented as a variational problem involving an explicit functional. Models with non-convex interactions are much less well-understood, and simple variational…

We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an…

The free energy of any system can be written as the supremum of a functional involving an energy term and an entropy term. Surprisingly, the limit free energy of mean-field spin glasses is expressed as an infimum instead, a phenomenon…

We develop a generalized TAP approach for the multi-species version of the spherical mixed $p$-spin models. In particular, we prove a generalized TAP representation for the free energy at any overlap vector which is multi-samplable in an…

We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with $D$ species, the Parisi formula is known to be valid, and expresses the limit free energy as a supremum over monotone…

We analyze models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have many remarkable symmetry properties as…

We prove that the free energy of any spherical mixed $p$-spin model converges as the dimension $N$ tends to infinity. While the convergence is a consequence of the Parisi formula, the proof we give is independent of the formula and uses the…

The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the purported solution. In this work we present a…

The limit free energy of an enriched mixed $p$-spin spin glass model has been identified with the solution of a Hamilton-Jacobi equation. In this note, we remark that the Aizenman-Sims-Starr scheme yields a subsolution to the equation.

We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational…

We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature…

We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…

We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy…

Inspired by a continuously increasing interest in modeling and framing complex systems in a thermody- namic rationale, in this paper we continue our investigation in adapting well known techniques (originally stemmed in fields of physics…