Optimization problems and replica symmetry breaking in finite connectivity spin glasses
نویسنده
چکیده
A formalism capable of handling the first step of hierarchical replica symmetry breaking (RSB) in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field distributions (or, equivalently magnetization distributions) inside the cluster of states. The approach is shown to coincide with previous works in the replica-symmetric case and in the two limiting cases m = 0 and 1 where m is Parisi’s break point. As an application to the study of optimization problems, the GS properties of the random 3-satisfiability problem are investigated and we present a first RSB solution improving replica-symmetric results.
منابع مشابه
Exact solutions for diluted spin glasses and optimization problems
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking ansatz we can solve exactly the saddle-point equations for graphs with uniform connectivity. The resulting ground state energy is in perfect agreement with numerical simulations. For fluctuating connectivity graphs, the ...
متن کاملFinite Dimensional Spin Glasses
We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry direct...
متن کامل2 9 A ug 2 00 1 The State ( s ) of Replica Symmetry Breaking : Mean Field Theories vs . Short - Ranged Spin Glasses ∗
We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another signature RSB feature — space filling relative domain walls between different finite-volume states. Thus revisions of the notion of pure states cannot shield...
متن کاملNumerical results for ground states of mean-field spin glasses at low connectivities
An extensive list of results for the ground-state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are being tested on mean-field models at low connectivity. Comparison with existing replica results for such models verifies the strength of those techniques. Y...
متن کاملLow Temperature Properties of Finite Dimensional Ising Spin Glasses: (some) Numerical Simulations
We review some recent results on finite dimensional spin glasses by studying recent numerical simulations and their relationship with experiments. In particular we will show results obtained at zero and non zero temperature, focusing in the low temperature properties of the model, and contrast them with different pictures of the low temperature phase of spin glasses: Replica Symmetry Breaking, ...
متن کامل