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We report progress in constructing Boltzmann weights for integrable 3-dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation can be conveniently parameterized in terms of N-th…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 G. von Gehlen , S. Pakuliak , S. Sergeev

We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition…

Mathematical Physics · Physics 2015-10-21 O. Foda , M. Wheeler

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a…

Strongly Correlated Electrons · Physics 2011-12-19 Alexander G. Abanov , Dmitri A. Ivanov , Yachao Qian

We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained…

Mathematical Physics · Physics 2014-04-15 M Wheeler

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently…

Mathematical Physics · Physics 2015-07-23 Filippo Colomo , Andrei G. Pronko

We discuss the functional Schroedinger picture for fermions in external fields for both stationary and time-dependent problems. We give formal results for the ground state and the solution of the time-dependent Schroedinger equation for QED…

High Energy Physics - Theory · Physics 2009-10-22 Claus Kiefer , Andreas Wipf

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…

Mathematical Physics · Physics 2009-10-31 P. Zinn-Justin

For a particular set of Boltzmann weights and a particular boundary condition for the six vertex model in statistical mechanics, we compute explicitly the partition function and show it to be equal to a factorial Schur function, giving a…

Combinatorics · Mathematics 2009-11-01 Peter J. McNamara

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of…

Mathematical Physics · Physics 2009-11-07 J. de Gier , V. Korepin

We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…

Mathematical Physics · Physics 2024-06-14 Mikhail D. Minin , Andrei G. Pronko , Vitaly O. Tarasov

In the present article we obtain the large $N$ asymptotics of the partition function $Z_N$ of the six-vertex model with domain wall boundary conditions on the critical line between the disordered and antiferroelectric phases. Using the…

Mathematical Physics · Physics 2012-09-03 Pavel Bleher , Thomas Bothner

In this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation graph'' and the ``$F$-matrix'': the…

Mathematical Physics · Physics 2022-11-15 Chenyang Zhong

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal…

Mathematical Physics · Physics 2017-11-06 Pavel Bleher , Karl Liechty

The determinantal form of the partition function of the 6-vertex model with domain wall boundary conditions was given by Izergin. It is known that for a special value of the crossing parameter the partition function reduces to a Schur…

Combinatorics · Mathematics 2014-02-20 Tiago Fonseca , Ferenc Balogh

Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions $F_\lambda,G_\lambda$…

Probability · Mathematics 2023-01-30 Amol Aggarwal , Alexei Borodin , Leonid Petrov , Michael Wheeler

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…

Mathematical Physics · Physics 2011-11-10 O. Foda , M. Wheeler , M. Zuparic

Partition function zeros are powerful tools in understanding critical behavior. In this paper we present new results of the Fisher zeros of two-dimensional Ising models, in the framework of free-fermion eight-vertex model. First we succeed…

Statistical Mechanics · Physics 2025-07-30 De-Zhang Li , Xin Wang

We obtain the large $n$ asymptotics of the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights $a=\sinh(\ga-t), b=\sinh(\ga+t), c=\sinh(2\ga),…

Mathematical Physics · Physics 2009-12-16 Pavel Bleher , Karl Liechty

We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their…

High Energy Physics - Theory · Physics 2009-10-28 Joakim Hallin , Per Liljenberg

In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional…

Mathematical Physics · Physics 2016-07-29 W. Galleas