Related papers: Metastates and Replica Symmetry Breaking
This thesis pretends to be another step in the development of numerical research in disordered systems. Specifically, we will focus on spin glasses which have demonstrated to be a fertile field from both, experimental and theoretical…
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,…
We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling…
The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition…
We consider short-range Ising spin glasses in equilibrium at infinite system size, and prove that, for fixed bond realization and a given Gibbs state drawn from a suitable metastate, each translation- and locally-invariant function (for…
We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $\beta_c$ implies the existence of an intermediate shattered phase. This confirms a prediction from physics regarding…
The metastable states of a glass are counted by adding a weak pinning field which explicitly breaks the ergodicity. Their entropy, that is the logarithm of their number, is extensive in a range of temperatures $T_G < T < T_C$ only, where…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
We study the Blume-Emery-Griffiths spin glass model in presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first…
We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…
Superstatistics is an elegant framework for the description of steady-state thermodynamics, mostly used for systems with long-range interactions such as plasmas. In this work, we show that the potential energy distribution of a classical…
The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between…
Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the…
In this letter we present a dynamical study of the structure of metastable states (corresponding to TAP solutions) in a mean-field spin-glass model. After reviewing known results of the statical approach, we use dynamics: starting from an…
We discuss the underlying connections among the thermodynamic properties of short-ranged spin glasses, their behavior in large finite volumes, and the interfaces that separate different pure states, and also ground states and low-lying…
A possible phase in short-range spin glasses exhibiting infinitely many equilibrium states is proposed and characterized in real space. Experimental signatures in equilibrating systems measured with scanning probes are discussed. Some…
The question of the number of thermodynamic states present in the low-temperature phase of the three-dimensional Edwards-Anderson Ising spin glass is addressed by studying spin and link overlap distributions using population annealing Monte…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
A simple geometrical characterization of configuration space neighborhoods of local energy minima in spin glass landscapes is found by exhaustive search. Combined with previous Monte Carlo investigations of thermal domain growth, it allows…
We study large deviations of the dynamical activity in the random orthogonal model (ROM). This is a fully connected spin-glass model with one-step replica symmetry breaking behaviour, consistent with the random first-order transition…