The Rotor Model and Combinatorics

Abstract

We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O($n=1$) model we find the number $A_{\mathrm{V}}(2m+1;3)$, which 3-enumerates vertically symmetric alternating sign matrices.

7 pages, Latex, WSPC macros, dedicated to Fred Wu's 70th birthday

References in corpus (7)

• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Combinatorial nature of ground state vector of O(1) loop model
• Spin chains and combinatorics: twisted boundary conditions
• Emptiness formation probability of the XXZ spin-1/2 Heisenberg chain at Delta=1/2
• Critical Q=1 Potts Model and Temperley-Lieb Stochastic Processes
• O(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices

Cited by in corpus (6)

• The raise and peel model of a fluctuating interface
• Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
• Different facets of the raise and peel model
• The Wave Functions for the Free-Fermion Part of the Spectrum of the $S{U}_q(N)$ Quantum Spin Models
• Fully packed loop models on finite geometries
• The Rotor Model with spectral parameters and enumerations of Alternating Sign Matrices