2016/02/24 by R. M. Liu, Weizhuang Zhuo, W. Z. Zhuo +10 · 17 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Computer science #Condensed matter physics #Critical point (mathematics) #Frustration #Ising model #Lattice (music) #Mathematics #Monte Carlo method #Phase transition #Physics #Physics of Superconductivity and Magnetism #Potts model #Square lattice #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #k-nearest neighbors algorithm
paper · pdf · doi:10.1103/physreve.93.032114
published in Physical review. E 93(3), 032114 (American Physical Society) · 20 pages, 10 figures. To be published in Physical Review E
arxiv created 2016/02/24 · openalex publication_date 2016/03/08 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work, we investigate the phase transitions and critical behaviors of the frustrated J(1)-J(2)-J(3) Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second-next-nearest-neighbor interaction J(3) on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller-like transition behavior in a certain range of J(3) is identified, while the four-state Potts-critical end point [J(3)/J(1)](C) is estimated based on the analytic method reported in earlier work [Jin, Sen, and Sandvik, Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction J(3) can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic J(3) can stabilize the staggered dimer state via a phase transition of strong first-order character.