O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices
Tóm tắt
This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.
Tài liệu tham khảo
A. V. Razumov and Yu. G. Stroganov, J. Phys. A, 34, 3185–3190 (2001); cond-mat/0012141 (2000).
M. T. Batchelor, J. de Gier, and B. Nienhuis, J. Phys. A, 34, L265–L270 (2001); cond-mat/0101385 (2001).
A. V. Razumov and Yu. G. Stroganov, J. Phys. A, 34, 5335–5340 (2001); cond-mat/0102247.
A. V. Razumov and Yu. G. Stroganov, Theor. Math. Phys., 138, 333–337 (2004); math.CO/0104216 (2001).
H. W. J. Bl¨ote and B. Nienhuis, J. Phys. A, 22, 1415–1438 (1989).
J. Propp, Discrete Math. Theor. Comput. Sci. (Proc.), AA, 43–58 (2001).
D. P. Robbins, “Symmetry classes of alternating sign matrices,” math.CO/0008045 (2000).
G. Kuperberg, Ann. Math., 156, 835–866 (2002); math.CO/0008184 (2000).
P. A. Pearce, V. Rittenberg, J. de Gier, “Critical Q = 1 Potts model and Temperley–Lieb stochastic processes,” cond-mat/0108051 (2001).