Superdiffusion-like behavior in zero-temperature coarsening of the d = 3 Ising model

Denis Gessert, Henrik Christiansen, Wolfhard Janke

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One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent α = 1/2 is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with α < 1/2 was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to L = 2048 employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth
law—but surprisingly, at still later times domains even grow superdifusively, i.e., with α > 1/2. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.
Original languageEnglish
Article number13270 (2023)
Number of pages8
JournalScientific Reports
Publication statusPublished - 15 Aug 2023

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This project was funded by the Deutsche Forschungsgemeinschaf (DFG, German Research Foundation) under project Nos. JA 483/33-1 and 189 853 844-SFB/TRR 102 (project B04), and the Deutsch-Französische Hochschule (DFH-UFA) through the Doctoral College “L4” under Grant No. CDFA-02-07. The n-fold way calculations were performed using the Sulis Tier 2 HPC platform hosted by the Scientific Computing Research Technology Platform at the University of Warwick. Sulis is funded by EPSRC Grant EP/T022108/1 and the HPC Midlands+ consortium.


  • Computational science
  • Ferromagnetism
  • Phase transitions and critical phenomena
  • Statistical physics


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