Height variables in the Abelian sandpile model: scaling fields and correlations
Height variables in the Abelian sandpile model: scaling fields and correlations
复制标题
DOI：
10.1088/1742-5468/2006/10/p10015
复制
发表时间：
2006-09
期刊：
影响因子：
--
通讯作者：
M. Jeng;Geoffroy Piroux;P. Ruelle
中科院分区：
文献类型：
--
作者：
M. Jeng;Geoffroy Piroux;P. Ruelle
我们计算了二维阿贝尔沙堆模型中四个高度变量在上半平面上的格点单点概率。当插入点远离边界时，以及当边界是开的或闭的时，我们找到了它们的精确缩放形式。与中心电荷c = −2的对数共形理论的预测相比，我们发现与以下场分配完全相容：高度2、3和4表现得像（一种不寻常的实现）标度维为2的主场的对数伙伴，主场本身与高度1变量相关联。有限尺寸的修正也计算和成功地与数值模拟相比。依靠这些领域的分配，我们制定了一个猜想的缩放形式的晶格两点相关的高度变量的平面上，这仍然是未知的。在这个系统中实现共形不变性的方式指向c = −2的局域场论，这与三重态理论不同。
We compute the lattice one-site probabilities, on the upper half-plane, of the four height variables in the two-dimensional Abelian sandpile model. We find their exact scaling form when the insertion point is far from the boundary, and when the boundary is either open or closed. Comparing with the predictions of a logarithmic conformal theory with central charge c = −2, we find a full compatibility with the following field assignments: the heights 2, 3 and 4 behave like (an unusual realization of) the logarithmic partner of a primary field with scaling dimension 2, the primary field itself being associated with the height 1 variable. Finite size corrections are also computed and successfully compared with numerical simulations. Relying on these field assignments, we formulate a conjecture for the scaling form of the lattice two-point correlations of the height variables on the plane, which remain as yet unknown. The way conformal invariance is realized in this system points to a local field theory with c = −2 which is different from the triplet theory.