Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation

TL;DR

This paper introduces a compartmental model for religious affiliation dynamics, analyzing phase transitions and absorbing states through analytical, numerical, and simulation methods, with real-world data comparison and the effect of inflexible individuals.

Contribution

The study develops a novel compartmental model incorporating social interactions, spontaneous transitions, and inflexible agents to analyze religious affiliation dynamics and phase transitions.

Findings

Existence of absorbing states where only one subpopulation survives.

Identification of two critical points affecting population coexistence.

Qualitative agreement with religious affiliation data from Northern Ireland.

Abstract

We propose a simple model to describe the dynamics of religious affiliation. For such purpose, we built a compartmental model with three distinct subpopulations, namely religious committed individuals, religious noncommitted individuals and not religious affiliated individuals. The transitions among the compartments are governed by probabilities, modeling social interactions among the groups and also spontaneous transitions among the compartments. First of all, we consider the model on a fully-connected network. Thus, we write a set of ordinary differential equations to study the evolution of the subpopulations. Our analytical and numerical results show that there is an absorbing state in the model where only one of the subpopulations survive in the long-time limit. There are also regions of parameters where some of the subpopulations coexist (two or three). We also verified the occurrence of two distinct critical points. In addition, we also present Monte Carlo simulations of the model on two-dimensional square lattices, in order to analyze the impact of the presence of a lattice structure on the critical behavior of the model. Comparison of the models' results with data for religious affiliation in Northern Ireland shows a good qualitative agreement. Finally, we considered the presence of inflexible individuals in the population, i.e., individuals that never change their states. The impact of such special agents on the critical behavior of the model is also discussed.