Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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LaTeX, 7 pages

Scientific paper

10.1088/0305-4470/34/26/301

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.

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