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  • Open Access

Absorbing phase transitions with memory in critical scaling

Kartik Chhajed1,* and P. K. Mohanty1,2,†

  • *Contact author: kartik@pks.mpg.de
  • †Contact author: pkmohanty@iiserkol.ac.in
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Phys. Rev. Research 8, 023156 – Published 11 May, 2026

DOI: https://doi.org/10.1103/jcby-h3pw

Abstract

Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally assumed that, conditioned on survival, their long-lived (quasistationary) behavior is unique and independent of the initial condition. We show that this need not hold, even for memoryless Markov dynamics. When the configuration space fractures into multiple macroscopic communicating classes, where configurations can be reached from one another within a class but not across classes, the system retains a measurable memory of its preparation, which can directly affect the critical exponents near absorbing transitions. Using a minimal birth-death-diffusion model, we demonstrate that the quasistationary state is unique when birth processes are present, but becomes nonunique and initial-condition dependent when they are suppressed. This mechanism, arising from vanishing of interclass escape-rate ratios in thermodynamic limit, challenges the conventional universality hypothesis and suggests possibility of history-dependent critical scaling in controlled lattice or colloidal systems with tunable particle number.

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Phys. Rev. Research 8, 023156– Published 11 May, 2026
  • Received 29 October 2025
  • Accepted 12 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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