Balog I, Uzelac K
Institute of Physics, P.O. Box 304, Bijenicka cesta 46, HR-10001 Zagreb, Croatia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011103. doi: 10.1103/PhysRevE.76.011103. Epub 2007 Jul 3.
The invaded cluster approach is extended to the two-dimensional Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the two-dimensional parameter space spanned by temperature and the chemical potential of the vacancies. The tricritical point is identified as a simultaneous onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of the "geometrical disorder cluster." The location of the tricritical point and the concentration of vacancies for q=1,2,3 are found to be in good agreement with the best known results. Scaling properties of the percolating scaling cluster and related critical exponents are also presented.
通过使用随机簇表示，将入侵簇方法扩展到具有退火空位的二维Potts模型。利用几何论证提出了一种算法，该算法收敛于由温度和空位化学势所跨越的二维参数空间中的三临界点。三临界点被确定为Fortuin-Kasteleyn簇的渗流和“几何无序簇”的渗流同时发生。发现对于q = 1、2、3，三临界点的位置和空位浓度与最知名的结果高度吻合。还给出了渗流标度簇的标度性质和相关的临界指数。
