# Symmetry breaking by heating in a continuous opinion model

## TL;DR

This paper investigates how social temperature and negative interactions influence opinion dynamics, revealing phase transitions and symmetry breaking phenomena with distinct universality classes in a continuous opinion model.

## Contribution

It introduces a comprehensive analysis of phase transitions in a continuous opinion model with positive and negative couplings and social temperature effects, identifying universality classes and novel phase behaviors.

## Key findings

- Symmetry breaking transition belongs to Ising mean-field universality class.
- Absorbing phase transitions have a critical exponent β=0.5, outside directed percolation.
- Ordered phases can emerge at higher social temperatures.

## Abstract

We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully-connected population. Opinions range in the real interval $[-1,1]$, representing the different shades of opinions against and for an issue under debate. Individual's opinions evolve through pairwise interactions, with couplings that are typically positive, but a fraction $p$ of negative ones is allowed. Moreover, a social temperature parameter $T$ controls the tendency of the individual responses towards neutrality. Depending on $p$ and $T$, different collective states emerge: symmetry broken (one side wins), symmetric (tie of opposite sides) and absorbing neutral (indecision wins). We find the critical points and exponents that characterize the phase transitions between them. The symmetry breaking transition belongs to the usual Ising mean-field universality class, but the absorbing-phase transitions, with $\beta=0.5$, are out of the paradigmatic directed percolation class. Moreover, ordered phases can emerge by increasing social temperature.