Related papers: One step replica symmetry breaking and overlaps be…
We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…
Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns…
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…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The…
We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
In Arguin & Tai (2018), the authors prove the convergence of the two-overlap distribution at low temperature for a randomized Riemann zeta function on the critical line. We extend their results to prove the Ghirlanda-Guerra identities. As a…
We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non…
We show that in the Sherrington-Kirkpatrick model at inverse temperature $\beta$ with uniform external field $h>0$, replica symmetry holds in the regime $ \beta^2\mathrm{E}[ \mathrm{sech}^4(\beta\sqrt{q}Z+h)] \le 1$, where $Z$ is a standard…
We propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x->0, x>>T of the Parisi replica symmetry…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
We prove the existence of full replica symmetry breaking (FRSB) for the Sherrington-Kirkpatrick (SK) model at low temperature. More specifically, we prove that slightly beyond the critical temperature, the Parisi measure for the SK model is…
In a previous work [A simplified Parisi Ansatz, Franchini, S., Commun. Theor. Phys., 73, 055601 (2021)] we introduced a simple method to compute the Random Overlap Structure of Aizenmann, Simm and Stars and the full RSB Parisi formula for…
In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…
We introduce a diagrammatic formulation for a cavity field expansion around the critical temperature. This approach allows us to obtain a theory for the overlap's fluctuations and, in particular, the linear part of the Ghirlanda-Guerra…
We study the overlap distribution of two particles chosen under the Gibbs measure at two temperatures for the branching Brownian motion. We first prove the convergence of the overlap distribution using the extended convergence of the…
There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on $[0,1]$, where the measure represents the similarity (or "overlap") of two independently sampled…