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Gaussian Mean Fields Lattice Gas

Mathematical Physics 2018-04-04 v2 math.MP Probability

Abstract

We study rigorously a lattice gas version of the Sherrington-Kirckpatrick spin glass model. In discrete optimization literature this problem is known as Unconstrained Binary Quadratic Programming (UBQP) and it belongs to the class NP-hard. We prove that the fluctuations of the ground state energy tend to vanish in the thermodynamic limit, and we give a lower bound of such ground state energy. Then we present an heuristic algorithm, based on a probabilistic cellular automaton, which seems to be able to find configurations with energy very close to the minimum, even for quite large instances.

Keywords

Cite

@article{arxiv.1711.03581,
  title  = {Gaussian Mean Fields Lattice Gas},
  author = {Benedetto Scoppola and Alessio Troiani},
  journal= {arXiv preprint arXiv:1711.03581},
  year   = {2018}
}

Comments

3 figures, 2 tables

R2 v1 2026-06-22T22:41:29.948Z