Agglomerative percolation on the Bethe lattice and the triangular cactus

作者：Chae Huiseung^*; Yook Soon Hyung; Kim Yup

来源：Journal of Physics A-Mathematical and Theoretical, 2013, 46(33): 335001.

DOI：10.1088/1751-8113/46/33/335001

Agglomerative percolation (AP) on the Bethe lattice and the triangular cactus is studied to establish the exact mean-field theory for AP. Using the self-consistent simulation method based on the exact self-consistent equations, the order parameter P-infinity and the average cluster size S are measured. From the measured P-infinity and S, the critical exponents beta(k) and gamma(k) for k = 2 and 3 are evaluated. Here, beta(k) and gamma(k) are the critical exponents for P-infinity and S when the growth of clusters spontaneously breaks the Z(k) symmetry of the k-partite graph. The obtained values are beta(2) = 1.79(3), gamma(2) = 0.88(1), beta(3) = 1.35(5) and gamma(3) = 0.94(2). By comparing these exponents with those for ordinary percolation (beta(infinity) = 1 and gamma(infinity) = 1), we also find beta(infinity) %26lt; beta(3) %26lt; beta(2) and gamma(infinity) %26gt; gamma(3) %26gt; gamma(2). These results quantitatively verify the conjecture that the AP model belongs to a new universality class if the Z(k) symmetry is broken spontaneously, and the new universality class depends on k.

• 出版日期2013-8-23