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Phase transitions in the frustrated Ising model on the square lattice

机译：方格上沮丧的Ising模型中的相变

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摘要

We consider the thermal phase transition from a paramagnetic to a stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J_1 ＜ 0 (nearest neighbor, ferromagnetic) and J_2 ＞ 0 (second neighbor, antiferromagnetic). The striped phase breaks a Z_4 symmetry and is stabilized at low temperatures for g = J_2/|J_1| ＞ 1/2. Despite the simplicity of the model, it has proved difficult to precisely determine the order and the universality class of the phase transitions. This was done convincingly only recently by Jin et al. [Phys. Rev. Lett. 108, 045702 (2012)]. Here, we further elucidate the nature of these transitions and their anomalies by employing a combination of cluster mean-field theory, Monte Carlo simulations, and transfer-matrix calculations. The J_1-J_2 model has a line of very weak first-order phase transitions in the whole region 1/2 ＜ g ＜ g~*, where g~* = 0.67 ±0.01. Thereafter, the transitions from g = g~* to g → ∞ are continuous and can be fully mapped, using universality arguments, to the critical line of the well-known Ashkin-Teller model from its four-state Potts point to the decoupled Ising limit. We also comment on the pseudo-first-order behavior at the Potts point and its neighborhood in the Ashkin-Teller model on finite lattices, which in turn leads to the appearance of similar effects in the vicinity of the multicritical point g* in the J_1-J_2 model. The continuous transitions near g~* can therefore be mistaken for first-order transitions, and this realization was the key to understanding the paramagnetic-striped transition for the full range of g ＞ 1/2. Most of our conclusions are based on Monte Carlo calculations, while the cluster mean-field and transfer-matrix results provide useful methodological benchmarks for weakly first-order behaviors and Ashkin-Teller criticality.
机译：我们在沮丧的二维方格伊辛模型中考虑竞争性相互作用J_1 ＜0（近邻，铁磁）和J_2＞ 0（第二近邻，反铁磁）时，考虑了从顺磁相到带反铁磁相的热相变。对于g = J_2 / | J_1 |，条纹相破坏了Z_4对称性并在低温下稳定。 ＞ 1/2。尽管该模型简单，但事实证明很难精确确定相变的顺序和通用性类别。只有Jin等人才令人信服地做到了这一点。 [物理牧师108，045702（2012）]。在这里，我们通过结合聚类平均场理论，蒙特卡洛模拟和转移矩阵计算来进一步阐明这些过渡及其异常的性质。 J_1-J_2模型在整个区域1/2 ＜g ＜g〜*处具有非常弱的一阶相变线，其中g〜* = 0.67±0.01。此后，从g = g〜*到g→∞的过渡是连续的，并且可以使用通用性参数完全映射到著名的Ashkin-Teller模型从其四态Potts点到解耦的Ising的临界线。限制。我们还评论了有限格上Ashkin-Teller模型中Potts点及其附近的伪一阶行为，这反过来导致在J_1的多临界点g *附近出现相似的效应。 -J_2模型。因此，接近g〜*的连续跃迁可能被误认为是一阶跃迁，而这一认识是理解g≥1/2整个范围内顺磁条纹跃迁的关键。我们的大多数结论都基于蒙特卡洛计算，而聚类平均场和转移矩阵结果为弱一阶行为和Ashkin-Teller临界度提供了有用的方法学基准。

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  • 来源
    《Physical review》 |2013年第14期|144406.1-144406.12|共12页
  • 作者

    Songbo Jin; Arnab Sen; Wenan Guo; Anders W. Sandvik;

  • 作者单位

    Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA;

    Max-Planck-lnstitut fuer Physik Komplexer Systeme, 01187 Dresden, Germany;

    Department of Physics, Beijing Normal University, Beijing 100875, China;

    Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA;

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  • 正文语种 eng
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  • 关键词

    nonequilibrium and irreversible thermodynamics; classical spin models;

    机译：非平衡和不可逆的热力学;经典自旋模型;

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