Quantum spin chains and Riemann zeta function with odd arguments

Apr, 2001
7 pages
Published in:
  • J.Phys.A 34 (2001) 5311-5316
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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.
Note:
  • LaTeX, 7 pages Subj-class: High Energy Physics - Theory; Statistical Mechanics; Mathematical Physics; Exactly Solvable and Integrable Systems
  • model: spin
  • ferromagnet
  • zeta function
  • correlation function
  • operator: vertex