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arXiv · 1711.03581

Gaussian Mean Fields Lattice Gas

Benedetto Scoppola·Alessio Troiani
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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.

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Benedetto Scoppola, Alessio Troiani. 2017-11-09. Gaussian Mean Fields Lattice Gas. https://doi.org/10.1007/s10955-018-1984-2

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