A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

TL;DR

This paper introduces a thermodynamic version of the Axelrod social influence model, analyzing its phase transition behavior and universality class in one dimension, revealing it behaves like a classical 1D thermodynamic system.

Contribution

It formulates a thermodynamic counterpart of the Axelrod model in 1D and analytically characterizes its critical properties and universality class.

Findings

Order-disorder transition occurs only at T=0

Model belongs to the same universality class as Ising and Potts models

Original Axelrod model with noise behaves like a thermodynamic 1D system

Abstract

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T = 0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.