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

TL;DR

This paper reviews recent exact results on pair-correlation functions and susceptibilities in various exactly solvable Ising models, including periodic, quasiperiodic, and frustrated systems, highlighting computational methods and potential future applications.

Contribution

It provides a comprehensive review of exact pair-correlation results and polynomial algorithms for susceptibilities in diverse Ising models, including new insights on frustrated and quasiperiodic systems.

Findings

Exact polynomial algorithms for susceptibilities in Z-invariant Ising models

Comparison of periodic and quasiperiodic Ising systems

Results on the fully-frustrated square-lattice Ising model

Abstract

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.