Related papers: Beyond Ising SK: m-vector, Potts, p-spin, spherica…
This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and…
In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs…
In 1975, two papers were published that together sparked major new directions, conceptual, mathematical and practically applicable, in several previously disparate fields of science. In this short review, we expose key aspects of their…
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock,…
I give a very brief non-technical introduction to the intersection of the fields of spin systems and computational complexity. The focus is on spin glasses and their relationship to NP-complete problems.
We include p-spin interactions in a spherical version of a soluble mean-field spin-glass model proposed by van Hemmen. Due to the simplicity of the solutions, which do not require the use of the replica trick, we are able to carry out a…
We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…
We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach…
The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control…
We reinterpret the Thouless-Anderson-Palmer approach to mean field spin glass models as a variational principle in the spirit of the Gibbs variational principle and the Bragg-Williams approximation. We prove this TAP-Plefka variational…
We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between $d$-dimensional quantum system with a $(d+1)$-dimensional…
A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
This is a review paper for the "Current Developments in Mathematics 2014" conference.
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range…
We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…
We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorization property of the optimal structures found by…
We consider the thermodynamics of an infinite-range Ising p-spin glass model with an additional r-spin ferromagnetic interaction. For r=2 there is a continuous transition to a ferromagnetic phase, while for r>2 the transition is first…
We present the first exact asymptotic characterization of sequential dynamics for a broad class of local update algorithms on the Sherrington-Kirkpatrick (SK) model with Ising spins. Focusing on dynamics implemented via systematic scan --…