Related papers: Boolean SK Model
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
We introduce a simple two-dimensional spin model with short-range interactions which shows glassy behavior despite a Hamiltonian which is completely homogeneous and possesses no randomness. We solve exactly for both the static partition…
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,…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of…
Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3-d spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up till the…
We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
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…
Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical…
We consider the Ising spin glass for the arbitrary spin S with the short- ranged interaction using the Bethe- Peierls approximation previously formulated by Serva and Paladin for the same system but limited to S=1/2. Results obtained by us…
We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between…
A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the…
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…
The Sherrington-Kirkpatrick (SK) is a foundational model for understanding spin glass systems. It is based on the pairwise interaction between each two spins in a fully connected lattice with quenched disordered interactions. The nature of…
In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a…