相关论文: Exact solutions for diluted spin glasses and optim…
We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
We analyze the properties of the energy landscape of {\it finite-size} fully connected $p$-spin-like models. In the thermodynamic limit the high temperature phase is described by the schematic Mode Coupling Theory of super-cooled liquids.…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs,…
We introduce and analytically study a generalized p-spin glass like model that captures some of the main features of attractive glasses, recently found by Mode Coupling investigations, such as a glass/glass transition line and dynamical…
The spherical $p$-spin is a fundamental model for glassy physics, thanks to its analytic solution achievable via the replica method. Unfortunately the replica method has some drawbacks: it is very hard to apply to diluted models and the…
Constraint Satisfaction Problems (CSPs) lie at the heart of complexity theory and find application in a plethora of prominent tasks ranging from cryptography to genetics. Classical approaches use Hopfield networks to find approximate…
In this paper, we investigate the finite connectivity spin-glass problem. Our work is focused on the expansion around the point of infinite connectivity of the free energy of a spin glass on a graph with Poissonian distributed connectivity:…
The search of hardware-compatible strategies for solving NP-hard combinatorial optimization problems (COPs) is an important challenge of today s computing research because of their wide range of applications in real world optimization…
We show that in the Ising pure $p$-spin model of spin glasses, shattering takes place at all inverse temperatures $\beta \in (\sqrt{(2 \log p)/p}, \sqrt{2\log 2})$ when $p$ is sufficiently large as a function of $\beta$. Of special interest…
We define a new family of random spin models with one-dimensional structure, finite-range multi-spin interactions, and bounded average degree (number of interactions in which each spin participates). Unfrustrated ground states can be…
We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids.…
In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the $p=2$ spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation…
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…