Jacques Perk - Oklahoma State University
Some Recent Results on Pair Correlation Functionsand Susceptibilities in Exactly Solvable Models
Detailed exact results on pair-correlation functions of Z-invariant models are still only available for Ising-type models. Using these we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. We shall 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, even fully-frustrated.
For the pentagrid Ising model we have developed a novel way of determining the pair probability of local environments on a Penrose tiling, which could also be used once more detailed results for pair correlations in e.g. the eight-vertex model or the chiral Potts model become available.
(Joint work with Helen Au-Yang, Oklahoma State University.)