Fourier Monte Carlo Simulation of Hexatic Membranes

Hexatic membranes are difficult to study both in theory as well as in simulations. We present new results for the flat phase of hexatic membranes using a unique simulation approach based on an recently developed optimization [1] of our Fourier Monte Carlo algorithm [2, 3] which enables us to drastically reduce critical slowing down and observe critical behavior with excellent statistical accuracy. In detail, we calculate the correlation function <vertical bar(f) over tilde (q)vertical bar >(2) = G(q) and the related mean squared displacement <(Delta f)(2)>) of the membrane's out-of-plane deformations in the Monge parametrization f (x) and give a finite size scaling analysis of these data. In our present treatment, the case of hexatic membranes is formally found to closely resemble that of solid membranes for which our algorithm has already proven to be quite successful [1].