95-287 Pierluigi Contucci, Andreas Knauf

The phase transition of the number-theoretical spin chain. (49K, latex) Jun 16, 95

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Abstract. In a previous paper one of us (A.K.) showed that the quotient Z(\beta):=\zeta(\beta-1)/\zeta(\beta) of Riemann zeta functions could be interpreted for \beta>2 as the canonical partition function of an infinite ferromagnetic spin chain. Here we prove that this model has exactly one phase transition, which is located at inverse temperature \beta_{crit}=2. There the magnetization jumps from one to zero. The energy density, being zero in the low temperature phase, grows at least linearly in \beta_{crit}-\beta.

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