de la Rocha André R, de Oliveira Paulo Murilo C, Arenzon Jeferson J
Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil.
Instituto Mercosul de Estudos Avançados, Universidade Federal da Integração Latino Americana, Foz do Iguaçu, Paraná, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042113. doi: 10.1103/PhysRevE.91.042113. Epub 2015 Apr 13.
A measure of cluster size heterogeneity (H), introduced by Lee et al. [Phys. Rev. E 84, 020101 (2011)] in the context of explosive percolation, was recently applied to random percolation and to domains of parallel spins in the Ising and Potts models. It is defined as the average number of different domain sizes in a given configuration and a new exponent was introduced to explain its scaling with the size of the system. In thermal spin models, however, physical clusters take into account the temperature-dependent correlation between neighboring spins and encode the critical properties of the phase transition. We here extend the measure of H to these clusters and, moreover, present new results for the geometric domains for both d=2 and 3. We show that the heterogeneity associated with geometric domains has a previously unnoticed double peak, thus being able to detect both the thermal and percolative transitions. An alternative interpretation for the scaling of H that does not introduce a new exponent is also proposed.
李等人[《物理评论E》84, 020101 (2011)]在爆发性渗流的背景下引入的一种团簇尺寸异质性度量(H)，最近被应用于随机渗流以及伊辛模型和Potts模型中平行自旋的畴。它被定义为给定构型中不同畴尺寸的平均数，并且引入了一个新的指数来解释其随系统尺寸的标度关系。然而，在热自旋模型中，物理团簇考虑了相邻自旋之间与温度相关的关联，并编码了相变的临界性质。我们在此将H的度量扩展到这些团簇，此外，还给出了二维和三维几何畴的新结果。我们表明，与几何畴相关的异质性具有一个先前未被注意到的双峰，因此能够检测热转变和渗流转变。还提出了一种对H标度关系的替代解释，该解释不引入新的指数。
