Universality of the triplet contact process with diffusion

TL;DR

This study uses GPU Monte Carlo simulations to analyze the critical behavior of the one-dimensional triplet contact process with diffusion, revealing deviations from mean field predictions and indicating non-mean field universality.

Contribution

The paper provides the first detailed numerical analysis showing that the TCPD model does not follow mean field behavior near criticality, challenging previous theoretical assumptions.

Findings

The ratio of pair to particle density tends to a constant near criticality.

Mean field prediction for the critical exponent δ is likely incorrect.

The critical exponent δ is estimated to be less than 0.32.

Abstract

The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density \rho and the density of pairs of neighboring particles \rho_p have been monitored as a function of time. Mean field predictions for the time evolution of these observables in the critical point are \rho\sim t^{-\delta} and \rho_p\sim t^{-\delta_p} with \delta=1/3 and \delta_p=2/3. We observe that in the vicinity of the critical point of the model, the ratio \rho_p/\rho tends to a constant, which shows that the one-dimensional TCPD model is not described by mean field behavior. Furthermore, our long simulations allow us to conclude that the mean field prediction of the exponent $\delta$ is almost certainly not correct either. Since the crossover to the critical regime is extremely slow for the TCPD model, we are unable to pinpoint a precise value for \delta, though we find as an upper bound \delta < 0.32.