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Gauge glass, spin glass and coding theory — exact results

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  • Nishimori, Hidetoshi

Abstract

A variety of exact and rigorous results are derived for statistical-mechanical models of gauge glasses and their generalizations. In particular, I prove the absence of gauge glass ordering in two dimensions at finite temperatures. I also calculate the exact value of the internal energy in a subspace of the phase diagram. A close relationship between the spin glass problem and coding theory is used to prove the conjecture of Ruján. That is, decoding of transmitted signals at a particular finite temperature is shown to have the smallest bit error rate. Most of these results are derived by a unified method of gauge transformation.

Suggested Citation

  • Nishimori, Hidetoshi, 1994. "Gauge glass, spin glass and coding theory — exact results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 1-14.
    • Handle: RePEc:eee:phsmap:v:205:y:1994:i:1:p:1-14
    DOI: 10.1016/0378-4371(94)90487-1
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    1. Kawamura, Shigekuni, 1993. "Japanese management style," Japan and the World Economy, Elsevier, vol. 5(3), pages 289-292, September.
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