124 research outputs found
A new representation for the partition function of the six vertex model with domain wall boundaries
We obtain a new representation for the partition function of the six vertex
model with domain wall boundaries using a functional equation recently derived
by the author. This new representation is given in terms of a sum over the
permutation group where the partial homogeneous limit can be taken trivially.
We also show by construction that this partition function satisfies a linear
partial differential equation.Comment: 14 pages, v2: added references, accepted for publication in J. Stat.
Mec
Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model
We solve the operator ordering problem for the quantum continuous integrable
su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum
trace identities, and the spectrum for the higher-order local charges. We also
show that this method, based on operator regularization and renormalization,
which guarantees quantum integrability, as well as the construction of
self-adjoint extensions, can be used as an alternative to the discretization
procedure, and unlike the latter, is based only on integrable representations.Comment: 27 pages; misprints corrected, references adde
The form factors in the finite volume
The form factors of integrable models in finite volume are studied. We
construct the explicite representations for the form factors in terms of
determinants.Comment: 16 pages, Latex, no figure
On the correlation functions of the domain wall six vertex model
We propose an (essentially combinatorial) approach to the correlation
functions of the domain wall six vertex model. We reproduce the boundary
1-point function determinant expression of Bogoliubov, Pronko and Zvonarev,
then use that as a building block to obtain analogous expressions for boundary
2-point functions. The latter can be used, at least in principle, to express
more general boundary (and bulk) correlation functions as sums over (products
of) determinants.Comment: LaTeX2e, requires eepic, 25 pages, including 29 figure
Norms of Bethe Wave Functions
Bethe Ansatz solvable models are considered, like XXZ Heisenberg
anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe
equation. The square of the norm of Bethe wave function is equal to a determinant of linearized
system of Bethe equations (determinant of matrix of second derivatives of Yang action). The proof
was first published in Communications in Mathematical Physics, vol 86, page 391 in l982. Also
domain wall boundary conditions for 6 vertex model were discovered in the same paper [see
Appendix D]. These play an important role for algebraic combinatorics: alternating sign matrices,
domino tiling and plane partition
Boundary correlation functions of the six-vertex model
We consider the six-vertex model on an square lattice with the
domain wall boundary conditions. Boundary one-point correlation functions of
the model are expressed as determinants of matrices, generalizing
the known result for the partition function. In the free fermion case the
explicit answers are obtained. The introduced correlation functions are closely
related to the problem of enumeration of alternating sign matrices and domino
tilings.Comment: 20 pages, 2 figures, typos correcte
Factorized domain wall partition functions in trigonometric vertex models
We obtain factorized domain wall partition functions for two sets of
trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2,
3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1)
Perk-Schultz models, for {r, s = \N}, where (given the symmetries of these
models) the result is independent of {r, s}.Comment: 12 page
On the domain wall partition functions of level-1 affine so(n) vertex models
We derive determinant expressions for domain wall partition functions of
level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing
parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil
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