Related papers: Partition function of the eight-vertex model with …
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.
We compute the continuum limit of the spectra for the XX-model with arbitrary complex boundary fields. In the case of hermitian boundary terms one obtains the partition functions of the free compactified boson field on a cylinder with…
We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation…
We write a multiple integral formula for the partition function of the Z-invariant six vertex model and demonstrate how it can be specialised to compute the norm of Bethe vectors. We also discuss the possibility of computing three-point…
We investigate the conjectured ground state eigenvector of the 8-vertex model inhomogeneous transfer matrix on its combinatorial line, i.e., at $\eta=\pi/3$, where it acquires a particularly simple form. We compute the partition function of…
A new recursive procedure for calculation of restricted partition function is suggested. An explicit formula for the restricted partition function is found based on this procedure.
Domain-wall fermions preserve chiral symmetry up to terms that decrease exponentially when the lattice size in the fifth dimension is taken to infinity. The associated rates of convergence are given by the low-lying eigenvalues of a simple…
The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a…
We study limit shapes in two equivalent models: the six-vertex model in the $c\to0$ limit and the random Mallows permutation with restricted permutation matrix. We give the Euler-Lagrange equation for the limit shape and show how to solve…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…
We study the interaction of particles with a domain wall at a symmetry-breaking phase transition by perturbing about the domain wall solution. We find the particulate excitations appropriate near the domain wall and relate them to the…
We will describe solvable lattice models whose partition functions depend on two sets of variables, $x_1,\cdots,x_n$ and $y_1, y_2, \cdots $ that have different connections with the representation theory of $\text{GL}(n,F)$ where $F$ is a…
We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition…
Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…
Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of three-choice polygons. We find that all the terms in the generating function can be reproduced from a linear…
Recently it was shown that the eigenfunctions for the the asymmetric exclusion problem and several of its generalizations as well as a huge family of quantum chains, like the anisotropic Heisenberg model, Fateev- Zamolodchikov model,…
We study a parameter optimization of domain-wall fermions to improve chiral symmetry based on machine learning. Domain-wall fermions involve coefficients along the fifth dimension, which can be treated as trainable parameters to reduce the…
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.