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 finite-size corrections with exponent ycan = 2yt - d both in energy-like and magnetic quantities, where yt = 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 non-universal. We confirm these predictions by extensive Monte Carlo simulations of the two-dimensional percolation problem which has ycan = -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.
Journal of Physics A Mathematical General
- Pub Date:
- December 2012
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks
- 19 pages, 4 figures