带有倾斜初始数据的 T 系统北极曲线

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Philippe Di Francesco, Hieu Trung Vu
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引用次数: 0

摘要

我们研究的是 A∞ 型 T 系统,也称为八面体递推/方程,被视为 2+1 维离散演化方程。根据早先从 "平 "初始数据八面体递归解中得到的阿兹特克钻石北极曲线的研究成果,我们考虑了垂直于任意可允许方向(r,s,t)∈Z+3 的平行 "斜 "平面的初始数据。T 系统的相应解被解释为 Bousquet-Mélou、Propp 和 West 于 2009 年引入的一些合适的 "松果 "图上的二聚体模型的分割函数。T 系统公式和一些均匀或周期情况下的精确解使我们能够探索相应二聚体模型的热力学极限,并推导出精确的北极曲线,将系统的不同阶段分开。这种直接方法绕过了使用卡斯特林矩阵方法的标准二聚体一般理论,而使用了多变量分析组合理论,重点研究了二聚体密度生成函数服从的线性系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Arctic curves of the T-system with slanted initial data
We study the T-system of type A , also known as the octahedron recurrence/equation, viewed as a 2+1 -dimensional discrete evolution equation. Generalizing earlier work on arctic curves for the Aztec Diamond obtained from solutions of the octahedron recurrence with ‘flat’ initial data, we consider initial data along parallel ‘slanted’ planes perpendicular to an arbitrary admissible direction (r,s,t)Z+3 . The corresponding solutions of the T-system are interpreted as partition functions of dimer models on some suitable ‘pinecone’ graphs introduced by Bousquet–Mélou, Propp, and West in 2009. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. This direct approach bypasses the standard general theory of dimers using the Kasteleyn matrix approach and uses instead the theory of Analytic Combinatorics in Several Variables, by focusing on a linear system obeyed by the dimer density generating function.
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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