Combinatorial Nature of the Ground-State Vector of the O(1) Loop Model
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Studying a possible connection between the ground-state vector for some special spin systems and the so-called alternating-sign matrices, we find numerical evidence that the components of the ground-state vector of the O(1) loop model coincide with the numbers of the states of the so-called fully packed loop model with fixed pairing patterns. The states of the latter system are in one-to-one correspondence with alternating-sign matrices. This allows advancing the hypothesis that the components of the ground-state vector of the O(1) loop model coincide with the cardinalities of the corresponding subsets of the alternating-sign matrices. In a sense, our conjecture generalizes the conjecture of Bosley and Fidkowski, which was refined by Cohn and Propp and proved by Wieland.
- A. V. Razumov and Yu. G. Stroganov, J. Phys. A, 34, 3185–3190 (2001); cond-mat/0012141.
- M. T. Batchelor, J. de Gier, and B. Nienhuis, J. Phys. A, 34, L265–L270 (2001); cond-mat/0101385.
- A. V. Razumov and Yu. G. Stroganov, J. Phys. A, 34, 5335–5340 (2001); cond-mat/0102247.
- H. W. J. Blöte, and B. Nienhuis, J. Phys. A, 22, 1415–1438 (1989).
- V. E. Korepin, A. G. Izergin, and N. M. Bogoliubov, Quantum Inverse Scattering Method, Correlation Functions, and Algebraic Bethe Ansatz, Cambridge Univ. Press, Cambridge (1993).
- R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, London (1982).
- J. Propp, Discrete Math. Theor. Comput. Sci. (Proc.), AA, 43–58 (2001); http://dmtcs.loria.fr/proceedings/ html/dmAA0103.abs.html.
- B. Wieland, Electron. J. Combin., 7, No. 1, R37 (2000); www.combinatorics.org.
- P. Lankaster, Theory of Matrices, Acad. Press, New York (1969).
- Combinatorial Nature of the Ground-State Vector of the O(1) Loop Model
Theoretical and Mathematical Physics
Volume 138, Issue 3 , pp 333-337
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- loop model
- ground state
- fully packed loop model
- alternating-sign matrices
- Industry Sectors