Persistence discontinuity in disordered contact processes with long-range interactions

TL;DR

This paper investigates how long-range interactions affect the persistence probability in disordered contact processes, revealing a discontinuous transition at the critical point for power-law decays.

Contribution

It introduces a combined approach using SDRG, phenomenological theory, and simulations to analyze persistence discontinuity in long-range disordered contact processes.

Findings

Persistence tends to a non-zero limit in the inactive phase and at criticality for power-law interactions.

Discontinuity in persistence at the critical point occurs only with power-law decays.

For stretched exponential decays, persistence remains continuous across the transition.

Abstract

We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization group (SDRG) method, a phenomenological theory of rare regions, and numerical simulations. We find that, for interactions decaying as an inverse power of the distance, the persistence probability tends to a non-zero limit not only in the inactive phase but also in the critical point. Thus, unlike in the contact process with short-range interactions, the persistence in the limit $t\to\infty$ is a discontinuous function of the control parameter. For stretched exponentially decaying interactions, the limiting value of the persistence is found to remain continuous, similar to the model with short-range interactions.