Temperature-Noise Interplay in a Coupled Model of Opinion Dynamics

TL;DR

This paper investigates how temperature-like and noise parameters influence opinion formation in a coupled Ising-voter model, revealing a simple relation at the phase transition and dominance of temperature dynamics at large group sizes.

Contribution

It provides a rigorous analytical framework and Monte Carlo simulations to understand the phase transition behavior in a coupled opinion dynamics model involving temperature and noise parameters.

Findings

Derived a simple relation T(p-a)=b at the critical line.

Identified conditions where temperature and noise are balanced.

Showed temperature dynamics dominate for large group sizes.

Abstract

We consider a coupled system mimicking opinion formation under the influence of a group of $q$ neighbors ($q$-lobby) that consists of an Ising part governed by temperature-like parameter $T$ and a voter dynamics parameterized by noise probability $p$ (independence of choice). Using rigorous analytical calculations backed by extensive Monte Carlo simulations, we examine the interplay between these two quantities. Based on the theory of phase transitions, we derive the relation between $T$ and $p$ at the critical line dividing the ordered and disordered phases, which takes a very simple and generic form $T(p-a)=b$ in the high temperature limit. For specific lobby sizes, we show where the temperature and noise are balanced, and we hint that for large $q$, the temperature-like dynamics prevails.