Abstract
We describe a universality class for the transitions of a generalized Pólya urn by studying the asymptotic behavior of the normalized correlation function using finite-size scaling analysis. are the successive additions of a red (blue) ball at stage and . Furthermore, represents the successive proportions of red balls in an urn to which, at the stage, a red ball is added with probability , and a blue ball is added with probability . A boundary exists in the plane between a region with one stable fixed point and another region with two stable fixed points for . with for , and is the (larger) value of the slope(s) of at the stable fixed point(s). On the boundary and for . The system shows a continuous phase transition for and behaves as with a universal function and a length scale with respect to . holds with and .
1 More- Received 10 June 2015
- Revised 6 October 2015
DOI:https://doi.org/10.1103/PhysRevE.92.052112
©2015 American Physical Society