Evaluation of Watson-like Integrals for Hyper bcc Antiferromagnetic Lattice

Details Evaluation of Watson-like Integrals for Hyper bcc Antiferromagnetic Lattice Evaluation of Watson-like Integrals for Hyper bcc Antiferromagnetic Lattice

2010-03-09

arxiv.org/abs/1003.1853v1

J. Phys. A: Math. Theor. 43 155206 (2010)

Physics

Mathematical Physics

13 pages, 2 figures, Accepted for publication in Journal of Physics A: Mathematical & Theoretical 2010

Scientific paper

10.1088/1751-8113/43/15/155206

Watson-like integrals for a d-dimensional bcc antiferromagnetic lattice I_d(\eta) and J_d(\eta) and another two similar integrals are evaluated in an exact way in terms of generalized hypergeometric functions. A simple formula connecting Id and Jd+1 is given along with the differential equations for I_d(\eta) and J_d(\eta). An application of I_d and J_d in the theory of the Heisenberg antiferromagnet is discussed, together with possible generalizations to non-integer values of d. Corresponding integrals for sc lattices are also briefly reviewed.

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