Percolation in the harmonic crystal and voter model in three dimensions.

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential U=(J2) summation operatorx,y[phi(x)-phi(y)]2, x,y Z3, J>0, and phi(x) R, a scalar height variable, and define occupation variables rhoh(x)=1 (0) for phi(x)>h (<h). The probability p of a site being occupied is then a function of h . In the voter model we consider a stationary measure in which each site is either occupied or empty, with probability p . In both cases the truncated pair correlation of the occupation variables, G(x-y) , decays asymptotically as mid |x-y|-1 . Using some Monte Carlo simulation methods and finite-size scaling we find accurate values of pc as well as the critical exponents for these systems. The latter are different from that of independent percolation in d=3 , as expected from the work of Weinrib and Halperin (WH) for the percolation transition of systems with G(r) approximately r-a [Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent nu is very close to the predicted value of 2, supporting the conjecture by WH that nu=2/a is exact.