Continuously variable spreading exponents in the absorbing Nagel-Schreckenberg model

TL;DR

This paper investigates a variant of the Nagel-Schreckenberg traffic model with an absorbing state, revealing a line of continuous phase transitions with variable critical exponents and compact active regions.

Contribution

It introduces and analyzes the absorbing Nagel-Schreckenberg model, showing continuously varying critical exponents along the phase transition line.

Findings

Active clusters are compact at long times.

Critical exponents delta and eta vary continuously along the transition line.

Exponents satisfy a hyperscaling relation for compact growth.

Abstract

I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel-Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between them and the car ahead. This makes the free-flow state (i.e., all vehicles traveling at the maximum speed, v_{max}, and with all headways greater than v_{max}) {\it absorbing}; such states are possible for for densities rho smaller than a critical value rho_c = 1/(v_{max} + 2). Drivers with nonzero velocity, and with headway equal to velocity, decelerate with probability p. This {\it absorbing Nagel-Schreckenberg} (ANS) model, introduced in [Phys. Rev. E {\bf 95}, 022106 (2017)], exhibits a line of continuous absorbing-state phase transitions in the rho-p plane. Here I study the propagation of activity from a localized seed, and find that the active cluster is compact, as is the active region at long times, starting from uniformly distributed activity. The critical exponents delta (governing the decay of the survival probability) and eta (governing the growth of activity) {\it vary continuously} along the critical line. The exponents satisfy a hyperscaling relation associated with compact growth.