Gauge glass, spin glass and coding theory — exact results

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.