Related papers: Boundary correlation functions of the six-vertex m…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting…
We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.
We consider multi-point correlation functions in the open XXZ chain with longitudinal boundary fields and in a uniform external magnetic field. We show that, at finite temperature, these correlation functions can be written in the quantum…
The connection between matrix integrals and links is used to define matrix models which count alternating tangles in which each closed loop is weighted with a factor n, i.e. may be regarded as decorated with n possible colors. For n=2, the…
The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free…
We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically…
The six-vertex model on a square lattice is "exactly solvable" because an exact formula for the free energy can be obtained by Bethe Ansatz. However, exact formulas for the correlations of local bulk observables, such as the orientation of…
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization…
The functional relations of the transfer matrices of fusion hierachies for six- and eight-vertex models with open boundary conditions have been presented in this paper. We have shown the su($2$) fusion rule for the models with more general…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
The general solutions for the factorization equations of the reflection matrices $K^{\pm}(\theta)$ for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are…
Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm…
We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…
In this work, we use the master function approach to describe the CFT limit of the six-vertex model at the free fermion point. Using the ODE/IM correspondence, we obtain an explicit form of the master function. This allows us to compute the…
With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and…
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…
The modulation is analyzed from the analytical properties of zeros of free fermionic partition function on the complex plane of wave numbers. It is shown how these properties are related to the oscillations of correlation functions. This…