Finite-size scaling of energylike quantities in percolation

We study the bond-percolation model in two and three dimensions by Monte Carlo simulation, and investigate the finite-size scaling behavior of several quantities that account for fluctuations of the total numbers of clusters and occupied bonds, N-c and N-b, respectively. These quantities include C-2c=(< N-c(2)>-< N-c >(2))/L-d and C-cb=(< NcNb >-< N-c >< N-b >)/L-d, where L is the linear system size and d is the spatial dimensionality. In statistical models with thermal fluctuations, C-2c and C-cb are specific heatlike quantities. Despite the absence of thermal fluctuations in percolation, we find that the leading finite-size scaling of C-2c and C-cb is described by the thermal critical exponent y(t)-d. We also measure quantity kappa(b)=2 < NbS2 >/< S-2 >-< NbS4 >/< S-4 >-< N-b > and an analogous quantity kappa(c) for N-c, where S-2 and S-4 are quantities associated with the second and the fourth moments of cluster sizes, respectively. At criticality, we show that kappa(b) and kappa(c) diverge as L-t(y) for L ->infinity. The analysis of the data of kappa(b) and kappa(c) yields y(t)=1.145(2) for the three-dimensional percolation, in good agreement with existing results.