Automatic contraction of unstructured tensor networks

Abstract

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local. Contents arXiv:1709.03080v3 [physics.comp-ph] 7 Aug 2019 J = −2 J = −1 J = −0.5 J = 0 J = 0.5 J = 1 J .0 J = −1.0 J = −0.5 J = 0.0 J = 0.5 J = 1.0 J = 2.0