Related papers: Spin-Glass Stochastic Stability: a Rigorous Proof
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is…
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero…
We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…
We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…
We prove that the Sherrington-Kirkpatrick model of spin glasses is chaotic under small perturbations of the couplings at any temperature in the absence of an external field. The result is proved for two kinds of perturbations: (a)…
We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of the Becchi-Rouet-Stora-Tyutin(BRST) supersymmetry. The Ward identities associated to this invariance indicate that the spin glass…
We consider the problem of temperature chaos in mean-field spin-glass models defined on random lattices with finite connectivity. By means of an expansion in the order parameter we show that these models display a much stronger chaos effect…
Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…
From the study of a functional equation relating the Gibbs measures at two different tempratures we prove that the specific entropy of the Gibbs measure of the Sherrington-Kirkpatrick Spin Glass Model vanishes at the inverse temperature…
After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour…
Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with…
We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We prove that, for any inverse temperature…
A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states, or theories that are based infinitely…
In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation…
In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
Spin glass models with quadratic-type Hamiltonians are disordered statistical physics systems with competing ferromagnetic and anti-ferromagnetic spin interactions. The corresponding Gibbs measures belong to the exponential family…