AI 中文总结
该研究针对二维热网格图上的Potts模型配分函数，通过转移矩阵热正则化分析不同q值下的递推阶，建立了图论组合学与物理环气模型表示理论的联系。
AI 中文摘要
我们研究二维热网格图上Potts模型配分函数的线性递推阶。通过将转移矩阵（TM）限制在实耦合轴上，物理算子在谱定理下保持可对角化。我们表明，这种热正则化使得Krylov子空间达到无约束平面状态容量，对于q≥4，递推阶锁定为反转后的Dyck路径（OEIS A007123）；对于q=3，由于有限指标Jones-Wenzl投影，递推阶坍缩为反转后的高度受限Dyck路径（OEIS A001998）；对于q=2，递推阶坍缩为零磁化守恒扇区（OEIS A001405）。该框架将图论组合学与物理环气模型的表示理论联系起来。
英文摘要
We study the linear recurrence order of the Potts model partition function on thermal 2D grid graphs. By restricting the transfer matrix (TM) to the real coupling axis, the physical operator maintains diagonalizability under the Spectral Theorem. We show that this thermal regularization allows the Krylov subspace to saturate the unconstrained planar state capacity, locking the recurrence order to the Dyck path up to reversal (OEIS A007123) for $q \ge 4$. Furthermore, the recurrence order collapses to height-restricted Dyck paths up to reversal (OEIS A001998) for $q=3$ due to finite-index Jones-Wenzl projections, and to the zero-magnetization conservation sector (OEIS A001405) for $q=2$. This framework bridges graph-theoretic combinatorics with the representation theory of physical loop gas models.
Comments28 pages, 2 figures, 3 tables
Journal refPhysica A: Statistical Mechanics and its Applications, 700 (2026) 131963
DOI：10.1016/j.physa.2026.131963
