Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNew differential equations in the six-vertex model
111
0
0.0
(
0
)
Authors
W. Galleas
Ask ChatGPT about the research
No Arabic abstract
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The models partition function is shown to obey a system of PDEs resembling the celebrated Knizhnik-Zamolodchikov equation. The analysis of our PDEs naturally produces a family of novel determinant representations for the models partition function.
rate research
Read More
In this work we elaborate on a previous result relating the partition function of the six-vertex model with domain-wall boundary conditions to eigenvalues of a transfer matrix. More precisely, we express the aforementioned partition function as a determinant of a matrix with entries being eigenvalues of the anti-periodic six-vertex models transfer matrix.
This paper is a continuation of our previous work Six-vertex model and non-linear differential equations I. Spectral problem in which we have put forward a method for studying the spectrum of the six-vertex model based on non-linear differential equations. Here we intend to elaborate on that approach and also discuss properties of the spectrum unveiled by the aforementioned differential formulation of the transfer matrixs eigenvalue problem. In particular, we intend to demonstrate how this differential approach allows one to study continuous symmetries of the transfer matrixs spectrum through the Lie groups method.
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the regime $Delta<1$. As an application, we provide a short, fully rigorous computation of the free energy of the six-vertex model on the torus, as well as an asymptotic expansion of the six-vertex partition functions when the density of up arrows approaches $1/2$. This latter result is at the base of a number of recent results, in particular the rigorous proof of continuity/discontinuity of the phase transition of the random-cluster model, the localization/delocalization behaviour of the six-vertex height function when $a=b=1$ and $cge1$, and the rotational invariance of the six-vertex model and the Fortuin-Kasteleyn percolation.
In this letter we show the partition function of the 8VSOS model with domain-wall boundaries satisfies the same type of functional equations as its six-vertex model counterpart. We then use these refined functional equations to obtain novel determinantal representations for the aforementioned partition function.
We describe a conjectural classification of Poisson vertex algebras of CFT type and of Poisson vertex algebras in one differential variable (= scalar Hamiltonian operators).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
