Non-glassy ground state in a long-range antiferromagnetic frustrated model in the hypercubic cell

Leonardo Franco and Sergio A Cannas

Physica A: Statistical Mechanics and its Applications, 2004, vol. 332, issue C, 337-348

Abstract: We analyzed the statistical mechanics of a long-range antiferromagnetic model defined on a D-dimensional hypercube, both at zero and finite temperatures. The associated Hamiltonian is derived from a recently proposed complexity measure of Boolean functions, in the context of neural networks learning processes. We show that, depending on the value of D, the system either presents a low-temperature antiferromagnetic stable phase or the global antiferromagnetic order disappears at any temperature. In the last case the ground state is an infinitely degenerated non-glassy one, composed by two equal size anti-aligned antiferromagnetic domains. We also present some results for the ferromagnetic version of the model.

Keywords: Ising model; Frustrated systems; Long-range interactions; Hypercubic cell; Boolean functions (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:332:y:2004:i:c:p:337-348

DOI: 10.1016/j.physa.2003.10.011

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