Related papers: Vector spin glasses with Mattis interaction II: no…
In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a…
In this work we want to enhance the calculation performed by Franz, Parisi and Virasoro (FPV) to estimate the free energy cost of interfaces in spin glasses and evaluate the lower critical dimension at which replica symmetry is restored. In…
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
The generalized Lotka-Volterra stochastic differential equation with a symmetric food interaction matrix is frequently used to model the dynamics of the abundances of the species living within an ecosystem when these interactions are…
We study the Hopfield model with pure $p$-spin interactions with even $p\geq 4$, and a number of patterns, M(N) growing with the system size, $N$, as $M(N) = \a N^{p-1}$. We prove the existence of a critical temperature $\b_p$ characterized…
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…
We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with +/- J interactions. We find that the energy of a…
In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…
The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…
The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is…
We present two rigorous results on the Sherrington-Kirkpatrick mean field model for spin glasses, proven by elementary methods, based on properties of fluctuations, with respect to the external quenched noise, of the thermodynamic variables…
The work of this thesis concerns the problem of linear low energy excitations of vector spin glass models. An analytical and numerical study is carried out, considering a fully connected random-field Heisenberg model at zero temperature, a…
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
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…
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 use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving…
Glassy behavior is one of the main open problems in condensed matter physics. In this thesis, we approach the problem by studying spin-glasses and colloids, using several complementary strategies. From the point of view of model building,…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…