Otsuka Hiromi
Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011140. doi: 10.1103/PhysRevE.80.011140. Epub 2009 Jul 29.
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.
我们讨论了在正方形晶格上定义的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微扰导致从二聚体液体到柱状相的贝雷津斯基 - 科斯特利茨 - Thouless 转变。根据野村和冈本对量子自旋链系统的讨论[《物理学报 A》27, 5773 (1994)]，我们提出了确定转变点的标准以及通用的能级分裂条件。随后，我们对高达由(L = 20)指定的线性维度的非对称实转移矩阵进行数值对角化计算，并确定全局相图。对于排斥区域，我们找到了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“零能量平带”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解释。
