Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs
Abstract
We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. Algorithms (SODA16), 514-527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.
Keywords
Cite
@article{arxiv.2005.07944,
title = {Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs},
author = {Martin Dyer and Marc Heinrich and Mark Jerrum and Haiko Müller},
journal= {arXiv preprint arXiv:2005.07944},
year = {2021}
}
Comments
Minor revisions. The version is accepted for publication in Combinatorics, Probability and Computing