Franz S, Leone M, Ricci-Tersenghi F, Zecchina R. Exact solutions for diluted spin glasses and optimization problems.
PHYSICAL REVIEW LETTERS 2001;
87:127209. [PMID:
11580554 DOI:
10.1103/physrevlett.87.127209]
[Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2001] [Indexed: 05/23/2023]
Abstract
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 same ansatz can be used in a variational way: For p-spin models (known as p-XOR-SAT in computer science) it provides the exact configurational entropy together with the dynamical and static critical connectivities (for p = 3, gamma(d) = 0.818, and gamma(s) = 0.918), whereas for hard optimization problems like 3-SAT or Bicoloring it provides new upper bounds for their critical thresholds ( gamma(var)(c) = 4.396 and gamma(var)(c) = 2.149).
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