Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
High Energy Physics - Theory
2008-11-26 v2 Statistical Mechanics
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/0104008,
title = {Quantum Spin Chains and Riemann Zeta Function with Odd Arguments},
author = {H. E. Boos and V. E. Korepin},
journal= {arXiv preprint arXiv:hep-th/0104008},
year = {2008}
}
Comments
LaTeX, 7 pages