Finite size scaling analysis of a nonequilibrium phase transition in the naming game model

TL;DR

This paper conducts a finite-size scaling analysis of a nonequilibrium phase transition in the noisy Naming Game model, revealing a discontinuous transition between consensus and fragmented states.

Contribution

It provides the first detailed numerical finite-size scaling analysis of the phase transition in the noisy Naming Game model, characterizing its discontinuous nature.

Findings

The phase transition is discontinuous, as indicated by scaling behavior.

The thermodynamic limit of the transition point is estimated.

Cluster size scaling supports the discontinuous transition hypothesis.

Abstract

We realize an extensive numerical study of the Naming Game model with a noise term which accounts for perturbations. This model displays a non-equilibrium phase transition between an absorbing ordered consensus state, which occurs for small noise, and a disordered phase with fragmented clusters characterized by heterogeneous memories, which emerges at strong noise levels. The nature of the phase transition is studied by means of a finite-size scaling analysis of the moments. We observe a scaling behavior typical of a discontinuous transition and we are able to estimate the thermodynamic limit. The scaling behavior of the clusters size seems also compatible with this kind of transition.