Related papers: Generalized Sherrington--Kirkpatrick-glass without…
The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable…
We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of…
We consider $N$ i.i.d. Ising spins with mean $m\in (-1,1)$ whose interactions are described by a Sherrington-Kirkpatrick Hamiltonian with a quartic correction. This model was recently introduced by Bolthausen in \cite{Bolt2} as a toy model…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
Framing the glass formation within standard statistical mechanics is an outstanding problem of condensed matter theory. To provide new insight, we investigate the structural properties of the Lennard-Jones fluid in the very-low temperature…
A key open question in the glass transition field is whether a finite temperature thermodynamic transition to the glass state exists or not. Recent simulations of coupled replicas in atomistic models have found signatures of a static…
We numerically study a disordered model for the RNA secondary structure and we find that it undergoes a phase transition, with a breaking of the replica symmetry in the low temperature region (like in spin glasses). Our results are based on…
An expansion for the free energy functional of the Sherrington-Kirkpatrick (SK) model, around the Replica Symmetric SK solution $Q^{({\rm RS})}_{ab} = \delta_{ab} + q(1-\delta_{ab})$ is investigated. In particular, when the expansion is…
We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here…
In this note, the Sherrington Kirkpatrick model of interacting spins is under consideration. In the high temperature region, we give an asymptotic expansion for the expected value of some genereral polynomial of the overlap of the system…
We present a first principle scheme to compute the rigidity, i. e. the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the…
In this article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to obtain simultaneously a symmetry breaking and a global…
We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann.~Probab.~43~(2015), no.~6, 3494--3513, where the author proved the Parisi formula under…
We review the approach to glasses based on the replica formalism. The replica approach presented here is a first principle's approach which aims at deriving the main glass properties from the microscopic Hamiltonian. In contrast to the old…
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting…
The Potts spin glass is an analogue of the Sherrington-Kirkpatrick model in which each spin can take one of $\kappa$ possible values, which we interpret as colors. It was suggested in arXiv:2310.06745 that the order parameter for this model…
Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking…