M.C.R.G. Study of Fixed-connectivity Surfaces

Abstract

We apply Monte Carlo Renormalization group to the crumpling transition in random surface models of fixed connectivity. This transition is notoriously difficult to treat numerically. We employ here a Fourier accelerated Langevin algorithm in conjunction with a novel blocking procedure in momentum space which has proven extremely successful in $λϕ^4$. We perform two successive renormalizations in lattices with up to $64^2$ sites. We obtain a result for the critical exponent $ν$ in general agreement with previous estimates and similar error bars, but with much less computational effort. We also measure with great accuracy $η$. As a by-product we are able to determine the fractal dimension $d_H$ of random surfaces at the crumpling transition.