Related papers: Balanced multi-species spin glasses

The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper,…

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…

We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on…

This paper constitutes the first part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this…

Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…

For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…

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 study the three-dimensional quantum Ising spin glass in a transverse magnetic field following the evolution of the bond probability distribution under Renormalisation Group transformations. The phase diagram (critical temperature $T_c$…

We study a p-spin spin-glass model to understand if the finite-temperature glass transition found in the mean-field regime of p-spin models, and used to model the behavior of structural glasses, persists in the non-mean-field regime. By…

We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\sigma) = \sigma^T J \sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles.…

In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…

The ferromagnetic Ising model on an $n\times n$ square lattice region $\Lambda$ with mixed boundary conditions can exhibit a phase transition as temperature varies. For this spin system, if we fix the spins on the top and bottom sides of…

We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…

It is generally believed (but not yet proved) that Ising spin glasses with nearest-neighbor interactions have a phase transition in three and higher dimensions to a low-temperature spin glass phase, but the nature of this phase remains…

We report large-scale simulations of the three-dimensional Edwards-Anderson Ising spin glass system using the recently introduced multi-overlap Monte Carlo algorithm. In this approach the temperature is fixed and two replica are coupled…

Mean field spin glass models have undergone substantial mathematical development, but finite dimensional short range spin glasses remain much less understood. This paper proves several rigorous zero temperature signatures of glassy behavior…

Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…

We consider the spherical Sherrington-Kirkpatrick model of spin glass with sparse interaction, where the interactions between most of the pairs of the spin variables are possibly zero. With suitable normalization, we prove that the limiting…

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…