Related papers: Replica symmetry breaking, complexity and spin rep…
In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random…
Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, {\it…
We determine explicit variational expressions for the free energy of mean-field spin glasses in a transversal magnetic field, whose glass interaction is given by a hierarchical Gaussian potential as in Derrida's Generalized Random Energy…
In order to study the activated dynamics of mean-field glasses, which takes place on times of order exp(N), where N is the system size, we introduce a new model, the Correlated Random Energy Model (CREM), that allows for a smooth…
We introduce a layered random spin model, equivalent to the Generalized Random Energy Model (GREM). In analogy with diluted spin systems, a diluted GREM (DGREM) is introduced.It can be applied to calculate approximately thermodynamic…
The random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and that their statistics satisfy the predictions of the…
A quadratic extension of REM has been treated. Discussed here is the origin of relation of REM to strings and other complex physical phenomena. Two basic features of the REM class of complex phenomena were identified: the double…
Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In a recent paper by L. Addario-Berry and the second author,…
In this thesis, we consider several Random Energy Models. This includes Derrida's Random Energy Model (REM) and Generalized Random Energy Model (GREM) and a nonhierarchical version (BK-GREM) by Bolthausen and Kistler. The limiting free…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on…
We compute the pressure of the random energy model (REM) and generalized random energy model(GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra's ``broken replica symmetry bounds",and…
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 study a generalization of the model introduced by Kistler and Schmidt in $2015$, that interpolates between the random energy model (REM) and the branching random walk (BRW). More precisely, we are interested in the asymptotic behaviour…
We introduce a mathematical framework based on simple combinatorial arguments (Kernel Representation) that allows to deal successfully with spin glass problems, among others. Let $\Omega^{N}$ be the space of configurations of an $N-$ spins…
We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with quenched random magnetic interaction. The thermodynamics is worked out in the Full Replica Symmetry…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
Motivated by the Lee--Yang approach to phase transitions, we study the partition function of the Generalized Random Energy Model (GREM) at complex inverse temperature $\beta$. We compute the limiting log-partition function and describe the…
We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho, da Costa and Yokoi (Phys. Rev. E 74 [2006]) who computed the free energy. In this…
We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by…
The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the…