On the Effect of Bottlenecks in Block Spin Models

TL;DR

This paper investigates how bottlenecks in a spin model influence phase transitions, identifying thresholds based on bottleneck size and interaction strength.

Contribution

It introduces multiple realizations of a bottleneck in a spin model and proves the existence of a threshold affecting phase transition behavior.

Findings

Existence of a threshold that determines the bottleneck's impact on phase transition

Threshold depends on bottleneck size and interaction strength

Different realizations of the bottleneck influence phase transition in the thermodynamic limit

Abstract

We study a bottleneck spin model with $N$ spins, split into two Curie-Weiss models at low temperature with a bottleneck between them. We propose multiple ways of how to realize such a bottleneck and study its influence on the phase transition in the thermodynamic limit $N \to \infty$. In all versions of this model we prove the existence of a threshold that determines whether or not the presence of the bottleneck is felt in the phase transition. This threshold depends on the size of the bottleneck and the interaction strength through it.