H E Boos and V E Korepin 2001 J. Phys. A: Math. Gen. 34 5311 doi:10.1088/0305-4470/34/26/301
H E Boos1 and V E Korepin2
Show affiliationsThe Riemann zeta function is an important object of number theory. We argue that it is related to the Heisenberg spin-1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in the thermodynamics limit. We prove that for short strings the probability can be expressed in terms of the Riemann zeta function with odd arguments.
02.10.De Algebraic structures and number theory
05.70.Ce Thermodynamic functions and equations of state
60Bxx Probability theory on algebraic and topological structures
82B30 Statistical thermodynamics (See also 80-XX)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 26 (6 July 2001)
Received 11 April 2001
Published 22 June 2001
H E Boos and V E Korepin 2001 J. Phys. A: Math. Gen. 34 5311
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