相关论文: Bounds for diluted mean-fields spin glass models
We study the SUSY-breaking complexity of the Bethe Lattice Spin-Glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For $J_{ij}=\pm 1$ the SUSY breaking theory yields…
The number $\langle N_s\rangle$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in…
Our goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure $p$-spin glasses above the replica…
Spin-models, where the $N$ spins interact pairwise with a $SU(n_f)$ symmetry preserving hamiltonian, famously simplify in the large $n_f$, $N$ limits, as derived by Sachdev and Ye when exploring mean-field behavior of spin-glasses. We…
We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the…
By means of parallel tempering Monte Carlo simulations we find strong evidence for a finite-temperature spin-glass transition in a system of diluted classical Heisenberg dipoles randomly placed on the sites of a simple cubic lattice. We…
In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…
This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
Shortened abstract: A mean field theory of long range frustration is constructed for spin glass systems with quenched randomness of vertex--vertex connections and of spin--spin coupling strengths. This theory is applied to a spin glass…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…
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)…
Spin glasses are models of statistical mechanics in which a large number of simple elements interact with one another in a disordered fashion. One of the fundamental results of the theory is the Parisi formula, which identifies the limit of…
In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the…
The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper,…
We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle…
This paper has been withdrawn because we have since found an analytic theory (arXiv:0712.3586) which shows that the dominant contribution to the free energy fluctuations comes from the region t\approx\tau. This regime was unfortunately…
The limit free energy of an enriched mixed $p$-spin spin glass model has been identified with the solution of a Hamilton-Jacobi equation. In this note, we remark that the Aizenman-Sims-Starr scheme yields a subsolution to the equation.
An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the {\beta} regime. In the original structural glass context this relationship follows from the MCT equations that are…
We study a finite range spin glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance $\gamma^{-1}$. We prove that, under a positivity condition for the interaction potential,…