Related papers: Contributions to Random Energy Models

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…

We introduce a natural nonhierarchical version of Derrida's generalized random energy model. We prove that, in the thermodynamical limit, the free energy is the same as that of a suitably constructed GREM.

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…

The complete phase diagram of Random Energy Model (REM) is obtained for complex temperatures using the method proposed by Derrida. We find the density of zeroes for statistical sum. Then the method is applied to Generalized Random Energy…

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…

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 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…

The Quantum Random Energy Model (QREM) is a random matrix of Anderson-type which describes effects of a transversal magnetic field on Derrida's spin glass. The model exhibits a glass phase as well as a classical and a quantum paramagnetic…

In this paper the Random Energy Model(REM) under exponential type environment is considered which includes double exponential and Gaussian cases. Limiting Free Energy is evaluated in these models. Limiting Gibbs' distribution is evaluated…

We introduce a nonlinear, nonhierarchical generalization of Derrida's GREM and establish through a Sanov-type large deviation analysis both a Boltzmann-Gibbs principle as well as a Parisi formula for the limiting free energy. In line with…

We establish both a Boltzmann-Gibbs principle and a Parisi formula for the limiting free energy of an abstract GREM (Generalized Random Energy Model) which provides an approximation of the TAP (Thouless-Anderson-Palmer) free energies…

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 extremes of a class of Gaussian fields with in-built hierarchical structure. The number of scales in the underlying trees depends on a parameter alpha in [0,1]: choosing alpha=0 yields the random energy model by Derrida (REM),…

In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is…

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. This was proven in a large class of models…

We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters.…

We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…

We consider a generalized version of the Random Energy Model in which the energy of each configuration is given by the sum of $N$ independent contributions ("local energies") with finite variances but otherwise arbitrary statistics. Using…

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. Here we give necessary conditions for this…

We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and…