Arctic curves of the octahedron equation
Arctic curves of the octahedron equation
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八面体方程的北极曲线
DOI：
10.1088/1751-8113/47/28/285204
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
R. Soto
中科院分区：
文献类型：
--
作者：
P. Francesco;R. Soto
我们研究了八面体关系（也称为A∞t系统），特别服从于Aztec菱形图的二聚体覆盖的配分函数。对于一类合适的双周期初始条件，我们得到了一个特别简单的分解形式的精确解。对于这些，我们证明了测量阿兹特克图面平均二聚体占用的密度函数服从具有周期系数的线性递归关系系统。这使我们能够探索相应二聚体模型的热力学极限，并推导出分离系统各个阶段的精确“北极”曲线。
We study the octahedron relation (also known as the A∞ T-system), obeyed in particular by the partition function for dimer coverings of the Aztec Diamond graph. For a suitable class of doubly periodic initial conditions, we find exact solutions with a particularly simple factorized form. For these, we show that the density function that measures the average dimer occupation of a face of the Aztec graph, obeys a system of linear recursion relations with periodic coefficients. This allows us to explore the thermodynamic limit of the corresponding dimer models and to derive exact ‘arctic’ curves separating the various phases of the system.