# Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses

@article{Zhou2007LongrangeFI, title={Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses}, author={Jie Zhou and Hui Ma and Haijun Zhou}, journal={arXiv: Disordered Systems and Neural Networks}, year={2007} }

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range…

## 5 Citations

Stability analysis on the finite-temperature replica-symmetric and first-step replica-symmetry-broken cavity solutions of the random vertex cover problem.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The stability of the finite-temperature replica-symmetric (RS) and the first-step replica-Symmetry-broken (1RSB) cavity solutions of the vertex cover problem on random regular graphs of finite vertex degree K are analyzed by population dynamics simulations.

Statistical and algebraic analysis of a family of random Boolean equations

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- 2009

The statistical and algebraic properties of a family of random Boolean equations are studied in this paper. Based on studying the mechanism of influence propagation from some variable fixed to 1, the…

Minimal Dominating Set problem studied by simulated annealing and cavity method: Analytics and population dynamics

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- 2017

The minimal dominating Set (MDS) problem is a prototypical hard combinatorial optimization problem. Two years ago we studied this problem by cavity method. Although we get the solution of a given…

Directed Dominating Set Problem Studied by Cavity Method: Warning Propagation and Population Dynamics

- Mathematics, PhysicsCommunications in Theoretical Physics
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The minimal dominating set for a digraph(directed graph)is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we…

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