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Exploring transition pathways in the Landau-Brazovskii model

Zhiyi Zhang1, Gang Cui2, Kai Jiang2, An-Chang Shi3, Pingwen Zhang1,4,*, Jianyuan Yin5,†, and Lei Zhang6,‡

  • 1School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 2Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
  • 3Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
  • 4School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 5School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, China
  • 6Beijing International Center for Mathematical Research, Center for Quantitative Biology, Center for Machine Learning Research, Peking University, Beijing 100871, China

  • *Contact author: pzhang@pku.edu.cn
  • †Contact author: jyyin@bnu.edu.cn
  • ‡Contact author: zhangl@math.pku.edu.cn
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Phys. Rev. Research 8, 013196 – Published 23 February, 2026

DOI: https://doi.org/10.1103/q4gq-dkkp

Abstract

The Landau-Brazovskii model provides a theoretical framework for describing various phases arising from competing short- and long-range interactions in many physical systems. In this work, we investigate phase transitions among various ordered phases within the three-dimensional Landau-Brazovskii model. We construct the phase diagram of this model, which encompasses eight distinct phases, and systematically compute the transition pathways connecting various metastable and stable states using the Landau-Brazovskii saddle dynamics. Along each transition pathway, the critical nucleus is identified with some detailed analyses of its shape, energy barrier, and Hessian eigenvalues. Furthermore, we explore how the transition state is influenced by model parameters, revealing systematic trends in critical nucleus sizes and energy barrier heights. Our results provide a comprehensive characterization of the nucleation mechanisms within the Landau-Brazovskii model and offer valuable insights into the structural transformations of modulated-phase systems.

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Phys. Rev. Research 8, 013196– Published 23 February, 2026
  • Received 19 October 2025
  • Accepted 15 January 2026
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