1,596 research outputs found

### Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models

Using detailed exact results on pair-correlation functions of Z-invariant
Ising models, we can write and run algorithms of polynomial complexity to
obtain wavevector-dependent susceptibilities for a variety of Ising systems.
Reviewing recent work we compare various periodic and quasiperiodic models,
where the couplings and/or the lattice may be aperiodic, and where the Ising
couplings may be either ferromagnetic, or antiferromagnetic, or of mixed sign.
We present some of our results on the square-lattice fully-frustrated Ising
model. Finally, we make a few remarks on our recent works on the pentagrid
Ising model and on overlapping unit cells in three dimensions and how these
works can be utilized once more detailed results for pair correlations in,
e.g., the eight-vertex model or the chiral Potts model or even
three-dimensional Yang-Baxter integrable models become available.Comment: LaTeX2e using iopart.cls, 10 pages, 5 figures (5 eps files), Dunk
Island conference in honor of 60th birthday of A.J. Guttman

### Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the
ground state sector eigenspace of the superintegrable tau_2(t_q) model is
highly degenerate and is generated by a quantum loop algebra L(sl_2).
Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2
algebras. For Q not equal 0, we shall show here that the corresponding
eigenspace of tau_2(t_q) is still highly degenerate, but splits into two
spaces, each containing 2^{r-1} independent eigenvectors. The generators for
the sl_2 subalgebras, and also for the quantum loop subalgebra, are given
generalizing those in the Q=0 case. However, the Serre relations for the
generators of the loop subalgebra are only proven for some states, tested on
small systems and conjectured otherwise. Assuming their validity we construct
the eigenvectors of the Q not equal 0 ground state sectors for the transfer
matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages,
uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added,
improvements and minor corrections made, erratum to paper 2 included. Version
3: Small paragraph added in introductio

### Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable
chiral Potts spin chain for chains of length 3,4,5. From these results we
present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update

### Spontaneous Magnetization of the Integrable Chiral Potts Model

We show how $Z$-invariance in the chiral Potts model provides a strategy to
calculate the pair correlation in the general integrable chiral Potts model
using only the superintegrable eigenvectors. When the distance between the two
spins in the correlation function becomes infinite it becomes the square of the
order parameter. In this way, we show that the spontaneous magnetization can be
expressed in terms of the inner products of the eigenvectors of the $N$
asymptotically degenerate maximum eigenvalues. Using our previous results on
these eigenvectors, we are able to obtain the order parameter as a sum almost
identical to the one given by Baxter. This gives the known spontaneous
magnetization of the chiral Potts model by an entirely different approach.Comment: LaTeX 2E document, using iopart.cls with iopams packages, 22 pages, 1
eps figure. Presented at the Simons Center for Geometry and Physics Workshop
on Correlation Functions for Integrable Models 2010: January 18-22, 2010.
Version 2: The identity conjectured in version 1 is now proved and its proof
is presented in arXiv:1108.4713; various small corrections and improvements
have been made als

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