### 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.

Original language | English |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 205 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1994 Apr 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

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## Cite this

Nishimori, H. (1994). Gauge glass, spin glass and coding theory - exact results.

*Physica A: Statistical Mechanics and its Applications*,*205*(1-3), 1-14. https://doi.org/10.1016/0378-4371(94)90487-1