Echo chambers in the Ising model and implications on the mean magnetization

TL;DR

This paper investigates the presence of echo chambers in the Ising model and related systems, revealing that symmetry properties determine their existence and developing an algorithm for magnetization calculation in tree networks.

Contribution

It classifies models based on symmetry to predict echo chambers and introduces an efficient algorithm for magnetization in tree-structured networks.

Findings

Ising model does not exhibit echo chambers due to symmetry.

Models with weak symmetry can have echo chambers with external fields.

Algorithm efficiently computes magnetization in tree networks.

Abstract

The echo-chamber effect is a common term in opinion dynamic modeling to describe how a person's opinion might be artificially enhanced as it is reflected back at her through social interactions. Here, we study the existence of this effect in statistical mechanics models, which are commonly used to study opinion dynamics. We show that the Ising model does not exhibit echo-chambers, but this result is a consequence of a special symmetry. We then distinguish between three types of models: (i) those with a strong echo-chamber symmetry, that have no echo-chambers at all; (ii) those with a weak echo-chamber symmetry that can exhibit echo-chambers but only if there are external fields in the system, and (iii) models without echo-chamber symmetry that generically have echo-chambers. We use these results to construct an efficient algorithm to efficiently and precisely calculate magnetization in arbitrary tree networks. Finally, We apply this algorithm to study two systems: phase transitions in the random field Ising model on a Bethe lattice and the influence optimization problem in social networks.