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