78 citations · 274 across the 28 of their papers we have counts for
31 papers
Personal History with MEF and Some Related Topics
Helen Au-Yang, Jacques H. H. Perk
We present our personal histories with Michael Fisher. We describe how each one of us first came to Cornell University. We also discuss our many subsequent interactions and success…
Spin-spin correlations in central rows of Ising models with holes
Helen Au-Yang, Jacques H. H. Perk
In our previous works on infinite horizontal Ising strips of width alternating with layers of strings of Ising chains of length , we found the surprising result that the spe…
Specific Heat of Ising Model with Holes: Mathematical Details Using Dimer Approaches
Helen Au-Yang, Jacques H. H. Perk
In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width connected by sequences of vertical strings of…
Integrable Chiral Potts Model and the Odd-Even Problem in Quantum Groups at Roots of Unity
Helen Au-Yang, Jacques H. H. Perk
At roots of unity the -state integrable chiral Potts model and the six-vertex model descend from each other with the model as the intermediate. We shall discuss how differ…
Ising Models with Holes: Crossover Behavior
Helen Au-Yang, Jacques H. H. Perk
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the ther…
Parafermions in the tau-2 model II
Helen Au-Yang, Jacques H. H. Perk
Many years ago Baxter introduced an inhomogeneous two-dimensional classical spin model, now called the model with free boundary conditions, and he specialized the resultin…
About 30 Years of Integrable Chiral Potts Model, Quantum Groups at Roots of Unity and Cyclic Hypergeometric Functions
Helen Au-Yang, Jacques H. H. Perk
In this paper we discuss the integrable chiral Potts model, as it clearly relates to how we got befriended with Vaughan Jones, whose birthday we celebrated at the Qinhuangdao meeti…
CSOS models descending from chiral Potts models: Degeneracy of the eigenspace and loop algebra
Helen Au-Yang, Jacques H. H. Perk
Monodromy matrices of the model are known to satisfy a Yang--Baxter equation with a six-vertex -matrix as the intertwiner. The commutation relations of the elements of the…
Parafermions in the tau-2 model
Helen Au-Yang, Jacques H. H. Perk
It has been shown recently by Baxter that the model with open boundary conditions can be solved by the "parafermionic" method of Fendley. In Baxter's paper there are sev…
Quasicrystals -- The impact of N.G. de Bruijn
Helen Au-Yang, Jacques H. H. Perk
In this paper we put the work of Professor N.G. de Bruijn on quasicrystals in historical context. After briefly discussing what went before, we shall review de Bruijn's work togeth…
Criticality in Alternating Layered Ising Models: II. Exact Scaling Theory
Helen Au-Yang
Part I of this article studied the specific heats of planar alternating layered Ising models with strips of strong coupling sandwiched between strips of weak coupling ,…
Criticality in Alternating Layered Ising Models : I. Effects of connectivity and proximity
Helen Au-Yang, Michael E. Fisher
The specific heats of exactly solvable alternating layered planar Ising models with strips of width lattice spacings and ``strong'' couplings sandwiched between strips…
Serre Relations in the Superintegrable Model
Helen Au-Yang, Jacques H. H. Perk
We derive the Serre relations for the generators of the quantum loop algebra L(sl_2) of the superintegrable tau_2 model in Q not 0 sectors, thus proving a fundamental conjecture in…
Superintegrable chiral Potts model: Proof of the conjecture for the coefficients of the generating function G(t,u)
Helen Au-Yang, Jacques H. H. Perk
In this paper, we prove the conjecture for the coefficients of the two variable generating function used in our previous paper. The conjecture was tested numerically before, but it…
Spontaneous Magnetization of the Integrable Chiral Potts Model
Helen Au-Yang, Jacques H. H. Perk
We show how -invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrab…
Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
Helen Au-Yang, Jacques H. H. Perk
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 genera…
Identities in the Superintegrable Chiral Potts Model
Helen Au-Yang, Jacques H. H. Perk
We present proofs for a number of identities that are needed to study the superintegrable chiral Potts model in the sector.
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
Jacques H. H. Perk, Helen Au-Yang
In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair…
Eigenvectors in the Superintegrable Model II: Ground State Sector
Helen Au-Yang, Jacques H. H. Perk
In 1993, Baxter gave eigenvalues of the transfer matrix of the -state superintegrable chiral Potts model with spin-translation quantum number , where $m_Q=\lfloor(N…
Eigenvectors in the Superintegrable Model I: sl_2 Generators
Helen Au-Yang, Jacques H H Perk
In order to calculate correlation functions of the chiral Potts model, one only needs to study the eigenvectors of the superintegrable model. Here we start this study by looking fo…
Yang-Baxter Equations
Jacques H. H. Perk, Helen Au-Yang
Preprint of an Encyclopedia article (Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 5…
Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models
Jacques H. H. Perk, Helen Au-Yang
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 susc…
Quasicrystals: Projections of 5-d Lattice into 2 and 3 Dimensions
Helen Au-Yang, Jacques H. H. Perk
We show that generalized Penrose tilings can be obtained by the projection of a cut plane of a 5-dimensional lattice into two dimensions, while 3-d quasiperiodic lattices with over…
Recent Developments on Ising and Chiral Potts Model
Jacques H. H. Perk, Helen Au-Yang
After briefly reviewing selected Ising and chiral Potts model results, we discuss a number of properties of cyclic hypergeometric functions which appear naturally in the descriptio…