Discontinuous phase transition in an open-ended Naming Game

TL;DR

This paper investigates a variant of the Naming Game on a 2D lattice, revealing a discontinuous phase transition between consensus and fragmentation driven by the variability of invented words.

Contribution

It introduces an open-ended Naming Game model with Gaussian-distributed word invention, identifying a discontinuous phase transition at a critical variability level.

Findings

Discontinuous phase transition at σ_c ≈ 25.6

Transition separates consensus and fragmented states

Finite-size scaling supports discontinuity

Abstract

In this work we study on a 2-dimensional square lattice a recent version of the Naming Game, an agent-based model used for describing the emergence of linguistic structures. The system is open-ended and agents can invent new words all along the evolution of the game, picking them up from a pool characterised by a Gaussian distribution with standard deviation $\sigma$. The model displays a nonequilibrium phase transition at a critical point $\sigma_{c}\approx 25.6$, which separates an absorbing consensus state from an active fragmented state where agents continuously exchange different words. The finite-size scaling analysis of our simulations strongly suggests that the phase transition is discontinuous.