Percolation in the canonical ensemble

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 y can = 2 y t − d both in energy-like 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 non-universal. We confirm these predictions by extensive Monte Carlo simulations of the two-dimensional 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.