Two Elliptic Height Models with Factorized Domain Wall Partition Functions
نویسندگان
چکیده
0.1. Factorization in trigonometric vertex models. In [1], we obtained factorized domain wall partition functions (DWPF’s) in two series of trigonometric vertex models: 1. The N -state Deguchi-Akutsu models, for N ∈ {2, 3, 4} (and conjectured the result for N ≥ 5), and 2. The gl(r+1|s+1) Perk-Schultz models, {r, s} ∈ N (where given the symmetries of these models, the result is independent of r and s).
منابع مشابه
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}. 0. Introduction Domain wall partition functions (DWPF’s) w...
متن کاملOn the Trigonometric Felderhof Model with Domain Wall Boundary Conditions
We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This de...
متن کاملSupersymmetric Vertex Models with Domain Wall Boundary Conditions
By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the gl(1|1) and gl(2|1) supersymmetric vertex models with domain wall boundary conditions. In the homogenous limit, these determinants degenerate to simple functions.
متن کاملSix - Vertex Model with Domain Wall Boundary Conditions and One - Matrix Model
The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on the phase. The expression is exact for finite lattice size, which is equal to the size of the corresponding matrix. In the thermodynamic limit, the matrix int...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کامل