Ising-like transitions in the O(n) loop model on the square lattice.
Ising-like transitions in the O(n) loop model on the square lattice.
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方晶格上 O(n) 循环模型中的类伊辛跃迁。
DOI：
10.1103/physreve.87.052118
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. Blöte
中科院分区：
文献类型：
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作者：
Z. Fu;Wenan Guo;H. Blöte
我们探讨了O（n）loop模型在（x，n）平面正方形格子上的相图，其中x是被loop覆盖的格子边的权。这些结果是基于传输矩阵计算和有限尺寸缩放。我们表示的相关长度与交错的环密度的传输矩阵的特征值。这个相关长度的有限大小的数据，结合标度公式，揭示了图中临界线的位置。对于n>>2，我们发现与基本回路的棋盘式排序的开始相关联的Ising样相变，即，最小可能的环，具有基本面的大小，其精确地覆盖最大环密度的正方形晶格的面的一半。在这方面，有序状态类似于最近邻排斥的硬正方形格子气，并且n的有限性表示其粒子-粒子势的软化。我们还确定了范围-2 n ≤2内的临界点。研究发现，相图的拓扑结构依赖于回路模型的允许顶点集。根据这个集合的选择，n>2的跃迁可以继续进入n≤2循环模型的稠密阶段，或者继续作为n≤2 O（n）多临界点的线。
We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points.