Pierluigi Contucci, Andreas Knauf
The phase transition of the number-theoretical spin chain.
(49K, latex)

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.