七角晶格上$q$态时钟模型的相变
Phase transition of $q$-state clock models on heptagonal lattices
摘要：
研究了负曲面上七角晶格上的$q$态时钟模型。我们发现，该系统具有三类平衡相，在有序和无序相之间，一个中间相，其特征在于在每一个$q \ge 2$观察到一个发散的磁化率与磁秩序。所有$q$的第三相的持久性与小$q$的平面系统中对应相的消失形成对比，这表明了七边形晶格中特有的非零表面积体积比的意义。基于Ginzburg-Landau理论和广义Cayley树的分析论证表明，本系统的两阶段跃迁归因于自旋波激发的能隙和强的边界自旋贡献。我们进一步证明了边界效应打破了体区域的平均场特征，这与无边界双曲晶格上的时钟模型的结果一致。
英文摘要：
We study the $q$-state clock models on heptagonal lattices assigned on a negatively curved surface. We show that the system exhibits three classes of equilibrium phases; in between ordered and disordered phases, an intermediate phase characterized by a diverging susceptibility with no magnetic order is observed at every $q \ge 2$. The persistence of the third phase for all $q$ is in contrast with the disappearance of the counterpart phase in a planar system for small $q$, which indicates the significance of nonvanishing surface-volume ratio that is peculiar in the heptagonal lattice. Analytic arguments based on Ginzburg-Landau theory and generalized Cayley trees make clear that the two-stage transition in the present system is attributed to an energy gap of spin-wave excitations and strong boundary-spin contributions. We further demonstrate that boundary effects breaks the mean-field character in the bulk region, which establishes the consistency with results of clock models on boundary-free hyperbolic lattices.
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