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, Nc and Nb, respectively. These quantities include C(2c) = (<N(2)c> - <Nc>2)/Ld and C(cb) = (<NcNb> - <Nc><Nb>)/Ld, 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> / <S2> - <NbS4> / <S4> - <Nb> and an analogous quantity kappa c for Nc, where S2 and S4 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(y)t 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.
Deng
Youjin
Y
Department of Physics, New York University, 4 Washington Square Place, New York, New York 10003, USA.
Yang
Xianqing
X