Percolation in the canonical ensemble

TL;DR

This paper investigates bond percolation in the canonical ensemble, revealing how fixing the number of occupied bonds affects finite-size corrections and universal parameters at criticality, supported by analytical and simulation results.

Contribution

It introduces an analytical framework for percolation in the canonical ensemble, showing the impact of constraints on finite-size corrections and universality.

Findings

Finite-size corrections with exponent y_{can}=2y_t-d at criticality.

Universal parameters mostly unchanged, but some amplitudes become non-universal.

Monte Carlo simulations confirm analytical predictions for 2D percolation.

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 finite-size corrections with exponent y_{can}=2y_t-d both in energy-like and magnetic quantities, where y_t=1/{\nu} is the thermal renormalization exponent and d is the spatial dimension. Furthermore, we find that while most of 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.