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

Author

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  • Franco, Leonardo
  • Cannas, Sergio A

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.

Suggested Citation

  • Franco, Leonardo & Cannas, Sergio A, 2004. "Non-glassy ground state in a long-range antiferromagnetic frustrated model in the hypercubic cell," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 337-348.
    • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:337-348
    DOI: 10.1016/j.physa.2003.10.011
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