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Frustrated Ising model on the honeycomb lattice: Metastability and universality

Denis Gessert1,2,*, Martin Weigel3,4, and Wolfhard Janke2

  • *Present address: Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
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Phys. Rev. B 113, 104436 – Published 18 March, 2026

DOI: https://doi.org/10.1103/gqwy-n84r

Abstract

We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths J1>0 and J2<0, respectively, on the honeycomb lattice. For J2>−J1/4 it has a ferromagnetic ground state, and previous work has shown that at least for J2≳−0.2J1 the transition is in the Ising universality class. For even lower J2 some indicators pointing towards a first-order transition were reported. By utilizing population annealing Monte Carlo simulations together with a rejection-free and adaptive update, we can equilibrate systems with J2 as low as −0.23J1. By means of a finite-size scaling analysis we show that the system undergoes a second-order phase transition within the Ising universality class at least down to J2=−0.23J1 and, most likely, for all J2>−J1/4. As we show here, there exist very long-lived metastable states in this system explaining the first-order like behavior seen in only partially equilibrated systems.

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Phys. Rev. B 113, 104436– Published 18 March, 2026
  • Received 4 September 2025
  • Revised 11 February 2026
  • Accepted 18 February 2026
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