Nonequilibrium phase transition in a model for the propagation of innovations among economic agents

TL;DR

This paper investigates a one-dimensional model of innovation spread among economic agents, revealing a nonequilibrium phase transition characterized by a roughening transition and unique critical behavior not fitting known universality classes.

Contribution

It demonstrates that the innovation propagation model exhibits a nonequilibrium surface growth transition with novel critical exponents and avalanche-driven dynamics.

Findings

Identifies a continuous roughening transition in the model.

Shows the transition does not belong to known universality classes.

Proposes avalanche dynamics as the cause of critical behavior.

Abstract

We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X.\ Guardiola, {\it et. al.}, Phys. Rev E {\bf 66}, 026121 (2002)]. We show that the model can be regarded as a nonequilibrium surface growth model. This allows us to demonstrate the presence of a continuous roughening transition between a flat (system size independent fluctuations) and a rough phase (system size dependent fluctuations). Finite-size scaling studies at the transition strongly suggest that the dynamic critical transition does not belong to directed percolation and, in fact, critical exponents do not seem to fit in any of the known universality classes of nonequilibrium phase transitions. Finally, we present an explanation for the occurrence of the roughening transition and argue that avalanche driven dynamics is responsible for the novel critical behavior.