Related papers: Critical behavior of random spin systems

In this paper we obtain two results for the Sherrington-Kirkpatrick (SK) model, and we show that they both emerge from a single approach. First, we prove that the average of the overlap takes positive values when it is non zero. More…

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…

Auffinger and Chen proved a variational formula for the free energy of the spherical bipartite spin glass in terms of a global minimum over the overlaps. We show that a different optimisation procedure leads to a saddle point, similar to…

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…

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…

We consider spin glass models with non-centered interactions and investigate the effect, on the random free energies, of flipping the interaction in a subregion of the entire volume. A fluctuation bound obtained by martingale methods…

In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an…

Extensive simulations are made of the spin glass susceptibility and correlation length in five dimension Ising Spin Glasses (ISGs) with Gaussian and bimodal interaction distributions. Once the transition temperature is accurately…

In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…

Using mappings to computer-science problems and by applying sophisticated algorithms, one can study numerically many problems much better compared to applying standard approaches like Monte Carlo simulations. Here, using calculations of…

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…

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all…

We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…

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 compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive…

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between…

In these notes, we continue our investigation of classical toy models of disordered statistical mechanics through various techniques recently developed and tested mainly on the paradigmatic SK spin glass. Here we consider the p-spin-glass…

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this…

We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value…

Extensive simulations are made of link and spin overlaps in four and five dimensional Ising Spin Glasses (ISGs). Moments and moment ratios of the mean link overlap distributions (the variance, the kurtosis and the skewness) show clear…