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Persistence properties of a phase-ordering system with competing dynamics

Shubham Thwal* and Suman Majumder†

  • Amity Institute of Applied Sciences, Amity University, Noida, Uttar Pradesh 201312, India

  • *Contact author: shubhamthwal1@gmail.com
  • †Contact author: smajumder@amity.edu, suman.jdv@gmail.com
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Phys. Rev. E 114, 044138 – Published 26 October, 2026

DOI: https://doi.org/10.1103/749x-1y96

Abstract

Understanding persistence properties of a system with respect to its underlying microscopic dynamics provides important insights into the associated first-passage behavior. Here, we investigate the persistence properties during phase ordering in the two-dimensional (d=2) Ising model evolving under competing nonconserved spin-flip and conserved spin-exchange dynamics by means of Monte Carlo simulations at zero temperature. We examine three distinct persistence probabilities: (i) the total persistence probability, defined as the probability that a lattice site has never experienced a change in the sign of the spin residing there; (ii) the spin-flip persistence probability, which exclusively measures the fraction of sites that have never undergone a spin-flip event; and (iii) the composite persistence probability, defined as the fraction of sites that have experienced neither a spin-flip nor a spin-exchange event. In the asymptotic regime, both the total and spin-flip persistence probabilities exhibit identical power-law decay, irrespective of the relative occurrence probability of the spin-flip move pr. The corresponding persistence exponent θi≈0.225, is found to be consistent with the value reported for systems evolving purely under nonconserved dynamics. We further demonstrate that both persistence measures satisfy the scaling relation d−dfi=θi/αi, where dfi is the fractal dimension of the corresponding persistence lattice and αi≈1/2 characterizes the asymptotic power-law growth of spatially correlated regions of nonpersistent spins. In contrast, although the composite persistence probability also exhibits asymptotic power-law decay, the corresponding persistence exponent θc and fractal dimension dfc of the persistence lattice show strong dependence on pr. Combined with the presence of a universal growth exponent αc≈1/2, this leads to the breakdown of the scaling relation among the characteristic exponents for the composite persistence.

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Phys. Rev. E 114, 044138– Published 26 October, 2026
  • Received 16 June 2026
  • Revised 4 September 2026
  • Accepted 13 October 2026
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