Related papers: Spin Distributions for Generic Spherical Spin Glas…
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,…
In this paper, we introduce a notion called "Approximate Ultrametricity" which encapsulates the phenomenology of a sequence of random probability measures having supports that behave like ultrametric spaces insofar as they decompose into…
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods…
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…
Our theoretical understanding of glassy dynamics is notoriously incomplete, and it is even more so when the glassy systems are driven out of equilibrium. An extreme way to drive a system out of equilibrium is to introduce nonequilibrium…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…
A new potential is presented for spherical galaxies. The technique of the construction of our model is similar to that given by An and Evans. In a special case, its mass density becomes a special one of the Hernquist model. Another special…
The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional…
A real space Renormalization Group approach is presented for a non-mean field spin-glass. This approach has been conceived in the effort to develop an alternative method to the Renormalization Group approaches based on the replica method.…
In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…
We study Gibbs distributions of spins taking values in a general compact Polish space, interacting via a pair potential along the edges of a generalized random graph with a given asymptotic weight distribution $P$, obtained by annealing…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…
We address the problem of spin-resolved scattering through spin-orbit nanostructures in graphene, i.e., regions of inhomogeneous spin-orbit coupling on the nanometer scale. We discuss the phenomenon of spin-double refraction and its…
In this work a short overview of the development of spin glass theories, mainly long and short range Ising models, are presented.
We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a…
Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous…