2D Ising Model with non-local links - a study of non-locality

TL;DR

This paper investigates how non-local links in 2D Ising models, inspired by quantum gravity considerations, affect phase transition temperatures and spin correlations, revealing that non-locality can significantly alter physical properties.

Contribution

It introduces a study of 2D Ising models with non-local links, connecting spin network non-locality to small world networks and analyzing their effects on critical behavior.

Findings

Non-local links raise the Curie temperature.

Configuration of non-local links impacts correlation functions.

Non-locality influences phase transition properties.

Abstract

Markopoulou and Smolin have argued that the low energy limit of LQG may suffer from a conflict between locality, as defined by the connectivity of spin networks, and an averaged notion of locality that emerges at low energy from a superposition of spin network states. This raises the issue of how much non-locality, relative to the coarse grained metric, can be tolerated in the spin network graphs that contribute to the ground state. To address this question we have been studying statistical mechanical systems on lattices decorated randomly with non-local links. These turn out to be related to a class of recently studied systems called small world networks. We show, in the case of the 2D Ising model, that one major effect of non-local links is to raise the Curie temperature. We report also on measurements of the spin-spin correlation functions in this model and show, for the first time, the impact of not only the amount of non-local links but also of their configuration on correlation functions.