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

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1016/j.physa.2003.10.011
arXiv ID: cond-mat/0302412
Source
arXiv
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Abstract

We analize 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 of 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.

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