Percolation in the canonical ensemble
Abstract
We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new finitesize corrections with exponent y_{can} = 2y_{t}  d both in energylike and magnetic quantities, where y_{t} = 1/ν is the thermal renormalization exponent and d is the spatial dimension. Furthermore, we find that while most of the universal parameters remain unchanged, some universal amplitudes, like the excess cluster number, can be modified and become nonuniversal. We confirm these predictions by extensive Monte Carlo simulations of the twodimensional percolation problem which has y_{can} = 1/2.
This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 December 2012
 DOI:
 10.1088/17518113/45/49/494006
 arXiv:
 arXiv:1210.3463
 Bibcode:
 2012JPhA...45W4006H
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 19 pages, 4 figures