 95287 Pierluigi Contucci, Andreas Knauf
 The phase transition of the numbertheoretical 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(\beta1)/\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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