摘要翻译：
我们研究了由包含Josephson$\pi$-结($\pi$-环）的环组成的平面团簇。每个$\pi$-环都带有一个持续的电流，表现为一个经典的轨道矩。与团簇处轨道矩的取向相关联的特定状态的类型取决于这些轨道矩之间的相互作用，并且可以很容易地控制，即通过偏置电流或其他方法。我们证明了这些体系可以用具有竞争最近邻和对角相互作用的二维Ising模型来描述，并研究了该模型的相图。基于五位正方形格子等小团簇的精确解和伊辛自旋无限正方形格子的平均场型方法，分析了该模型的特征。并与Monte Carlo模拟得到的100×100平方晶格的自旋图和实验结果进行了比较。我们表明，$\pi$-环团簇可以作为一种新型的超导存储元件。所得结果可在实验中得到验证，并适用于量子态随耦合常数的缓慢变化而绝热切换的绝热量子计算。
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英文标题：
《Two-dimensional Ising model with competing interactions and its
  application to clusters and arrays of $\pi$-rings and adiabatic quantum
  computing》
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作者：
A. O'Hare, F.V. Kusmartsev, K.I. Kugel, and M.S. Laad
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Strongly Correlated Electrons        强关联电子
分类描述：Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学，非费米液体，自旋液体，量子临界性，电荷密度波，金属-绝缘体跃迁
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We study planar clusters consisting of loops including a Josephson $\pi$-junction ($\pi$-rings). Each $\pi$-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments at the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. We show that these systems can be described by the two-dimensional Ising model with competing nearest-neighbor and diagonal interactions and investigate the phase diagram of this model. The characteristic features of the model are analyzed based on the exact solutions for small clusters such as a 5-site square plaquette as well as on a mean-field type approach for the infinite square lattice of Ising spins. The results are compared with spin patterns obtained by Monte Carlo simulations for the 100 $\times$ 100 square lattice and with experiment. We show that the $\pi$-ring clusters may be used as a new type of superconducting memory elements. The obtained results may be verified in experiments and are applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constants.
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PDF链接：
https://arxiv.org/pdf/705.1643