How to experimentally probe universal features of absorbing phase transitions using steady state

TL;DR

This paper proposes experimental methods to analyze universal features of absorbing phase transitions, focusing on interval distributions and correlation measurements in flowing systems, supported by numerical validations and bias correction techniques.

Contribution

It introduces new approaches for probing universal features of absorbing phase transitions through interval distribution analysis and correlation length measurements in flowing systems.

Findings

Universal scaling of interval distributions confirmed with bias correction.

Correlation length and time can be measured via decay length in flowing systems.

Identification of crossover behaviors and associated scaling laws.

Abstract

We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of duration/length of intervals of local inactive state in quasi-steady state, which has been very commonly used in experiments, in a case of the contact process. We show that the distributions obey the universal scaling ansatz expected from phenomenological scaling argument, but that care must be taken in order to suppress a bias caused by censoring due to a finite observation window. To demonstrate the latter point, we compare the distributions for the temporal intervals estimated through conventional histograms with those through the estimator which properly takes account of censoring and sampling bias. On the other hand, we also propose that, if a system is subject to uniform advection as is often the case with flowing systems, a correlation length and a correlation time near the transition point can be easily quantified by supplying the system with an active boundary condition. In order to support our proposal, we introduce a new model whose advection strength can be arbitrarily controlled. The results of numerical simulations on our model suggest that a correlation time, which is difficult to measure through the interval distributions without the aforementioned bias, can be measured through characteristic decay length of an order parameter. Crossovers between two different power-law behaviors are also identified in this case, and the universal scaling ans\"{a}tze associated with the crossovers are discussed.