A V Razumov and Yu G Stroganov J. Stat. Mech. (2006) P07004 doi:10.1088/1742-5468/2006/07/P07004
Bethe roots and refined enumeration of alternating-sign matrices
FREE ARTICLE Topical articles on The 75th Anniversary of the Bethe AnsatzA V Razumov and Yu G Stroganov
Show affiliationsPart of Topical articles on The 75th Anniversary of the Bethe Ansatz
The properties of the most probable ground state candidate for the XXZ spin chain with the anisotropy parameter equal to −1/2 and an odd number of sites is considered. Some linear combinations of the components of the state considered, divided by the maximal component, coincide with the elementary symmetric polynomials in the corresponding Bethe roots. It is proved that these polynomials are equal to the numbers providing the refined enumeration of the alternating-sign matrices of order M+1 divided by the total number of the alternating-sign matrices of order M, for the chain of length 2M+1.
- Keywords
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E-print Number: math-ph/0605004
Cited: by |
Refers: to
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 07 (July 2006)
Received 20 May 2006, accepted for publication 23 June 2006
Published 13 July 2006
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Bethe roots and refined enumeration of alternating-sign matrices
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