Gaussian Mean Field Lattice Gas |
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Authors: | Benedetto Scoppola Alessio Troiani |
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Institution: | 1.Dipartimento di Matematica,Università degli Studi di Roma “Tor Vergata”,Rome,Italy;2.Dipartimento di Matematica e Informatica “Ulisse Dini”,Università degli Studi di Firenze,Florence,Italy |
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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 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 a 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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