  Riemann zeta function is an important object of number theory. It was also
used for description of disordered systems in statistical mechanics. We show
that Riemann zeta function is also useful for the description of integrable
model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a
probability of formation of a ferromagnetic string in the anti-ferromagnetic
ground state in thermodynamics limit. We prove that for short strings the
probability can be expressed in terms of Riemann zeta function with odd
arguments.
