Echo chambers in the Ising model and implications on the mean magnetization
Abstract
The echochamber 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 echochambers, but this result is a consequence of a special symmetry. We then distinguish between three types of models: (i) those with a strong echochamber symmetry, that have no echochambers at all; (ii) those with a weak echochamber symmetry that can exhibit echochambers but only if there are external fields in the system, and (iii) models without echochamber symmetry that generically have echochambers. 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.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 April 2022
 DOI:
 10.1088/17425468/ac5d42
 arXiv:
 arXiv:2201.00149
 Bibcode:
 2022JSMTE2022d3402B
 Keywords:

 general equilibrium models;
 Condensed Matter  Statistical Mechanics;
 Physics  Physics and Society
 EPrint:
 20 pages, 4 figures