Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling limit of the ${cal Z}_2$ invariant inhomogeneous six-vertex model
58
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged ${rm SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur.
rate research
Read More
The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses ${rm U}(1)$ invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of ${cal C}$, ${cal P}$ and ${cal T}$ as well as translational invariance. The special properties of the lattice system that possesses an additional ${cal Z}_r$ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.
Based on the results published recently [J. Phys. A: Math. Theor. 50, 065201 (2017)], the universal finite-size contributions to the free energy of the square lattice Ising model on the $Ltimes M$ rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit $L,Mtoinfty$, $Tto T_mathrm{c}$, with fixed temperature scaling variable $xpropto(T/T_mathrm{c}-1)M$ and fixed aspect ratio $rhopropto L/M$. We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point $T=T_mathrm{c}$ we confirm predictions from conformal field theory by Cardy & Peschel [Nucl. Phys. B 300, 377 (1988)] and by Kleban & Vassileva [J. Phys. A: Math. Gen. 24, 3407 (1991)]. The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.
The spin-1/2 highest weight representations of the dynamical 6-vertex and the standard 8-vertex Yang-Baxter algebra on a finite chain are considered in this paper. For the antiperiodic dynamical 6-vertex transfer matrix defined on chains with an odd number of sites, we adapt the Sklyanins quantum separation of variable (SOV) method and explicitly construct SOV representations from the original space of representations. We provide the complete characterization of eigenvalues and eigenstates proving also the simplicity of its spectrum. Moreover, we characterize the matrix elements of the identity on separated states by determinant formulae. The matrices entering in these determinants have elements given by sums over the SOV spectrum of the product of the coefficients of separate states. This SOV analysis is not reduced to the case of the elliptic roots of unit and the results here derived define the required setup to extend to the dynamical 6-vertex model the approach recently developed in [1]-[5] to compute the form factors of the local operators in the SOV framework, these results will be presented in a future publication. For the periodic 8-vertex transfer matrix, we prove that its eigenvalues have to satisfy a fixed system of equations. In the case of a chain with an odd number of sites, this system of equations is the same entering in the SOV characterization of the antiperiodic dynamical 6-vertex transfer matrix spectrum. This implies that the set of the periodic 8-vertex eigenvalues is contained in the set of the antiperiodic dynamical 6-vertex eigenvalues. A criterion is introduced to find simultaneous eigenvalues of these two transfer matrices and associate to any of such eigenvalues one nonzero eigenstate of the periodic 8-vertex transfer matrix by using the SOV results. Moreover, a preliminary discussion on the degeneracy of the periodic 8-vertex spectrum is also presented.
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.
The probability that a point is to one side of a curve in Schramm-Loewner evolution (SLE) can be obtained alternatively using boundary conformal field theory (BCFT). We extend the BCFT approach to treat two curves, forming, for example, the left and right boundaries of a cluster. This proves to correspond to a generalisation to SLE(kappa,rho), with rho=2. We derive the probabilities that a given point lies between two curves or to one side of both. We find analytic solutions for the cases kappa=0,2,4,8/3,8. The result for kappa=6 leads to predictions for the current distribution at the plateau transition in the semiclassical approximation to the quantum Hall effect.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
