Classical dimer model with anisotropic interactions on the square lattice.
Classical dimer model with anisotropic interactions on the square lattice.
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方形晶格上具有各向异性相互作用的经典二聚体模型。
DOI：
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发表时间：
2009
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通讯作者：
H. Otsuka
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作者：
H. Otsuka
本文讨论了正方形晶格上具有各向异性相互作用的经典二聚体模型的相变和相图。对于吸引区域，由各向异性引入的取向序参量的扰动导致从二聚体-液体到柱状相的Berezinskiii-Kosterlitz-无规转变。根据Nomura和Okamoto对量子自旋链系统的讨论[J. Phys. A 27，5773（1994）]，我们给出了确定跃迁点的判据和普遍的能级分裂条件。随后，我们进行数值对角化计算的非对称的真实的传输矩阵的线性尺寸指定L=20，并确定全球相图。对于排斥区域，我们发现二聚体液体和强排斥相之间的边界。基于在强排斥极限下呈现双重“零能平带”的单弦运动的色散关系，我们对强排斥相的性质给出了直观的解释。
We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a twofold "zero-energy flat band" in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.