npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041
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Research Paper

New Phys.: Sae Mulli 2020; 70: 613-617

Published online July 31, 2020 https://doi.org/10.3938/NPSM.70.613

Copyright © New Physics: Sae Mulli.

Driven Contact Process with Temporal Feedback

Meesoon HA*

Department of Physics Education, Chosun University, Gwangju 61452, Korea

Correspondence to:msha@chosun.ac.kr

Received: April 30, 2020; Revised: May 25, 2020; Accepted: June 4, 2020

Abstract

We investigate a directed percolation (DP)-based cyclically coupled model with branching bias, namely, the driven contact process with temporal feedback (DCP-TF). In the DCP-TF, we control not only the temporal feedback by using its memory strength and the power-law tail exponent for the incubation period of the intermediate state but also the preferred direction of branching. The CP-TF in a one-dimensional lattice exhibits continuously varying scaling behaviors, which is attributed to the long-term memory caused by the power-law type feedback. This implies that the CP-TF does not belong to the DP universality class. However, its deviation from the DP exponent is not very big. To clarify this issue, we test the relevance of the external driving to the critical behaviors of CP-TF. If it belongs to the DP universality class, the branching bias is irrelevant to its critical exponents. We find that the branching bias does affect both the region of continuously varying scaling and the value of critical decay exponent. Based on numerical results and intuitive arguments in the DCP-TF, we discuss how the universality class of the CP-TF is related to the universality class of the pair CP with diffusion.

Keywords: Nonquilibrium phase transitions, Contact process, Directed percolation, Long-term memory, Diffusion/branching bias, Universality class

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