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

## TL;DR

This study uses advanced Monte Carlo Renormalization Group techniques with novel algorithms to analyze the crumpling transition in fixed-connectivity random surfaces, achieving accurate critical exponents with reduced computational effort.

## Contribution

Introduces a Fourier accelerated Langevin algorithm and a new momentum space blocking procedure for efficient analysis of the crumpling transition.

## Key findings

- Critical exponent ν in agreement with previous estimates
- Precise measurement of the exponent η
- Determination of the fractal dimension d_H at the transition

## 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 $\lambda\phi^4$. We perform two successive renormalizations in lattices with up to $64^2$ sites. We obtain a result for the critical exponent $\nu$ in general agreement with previous estimates and similar error bars, but with much less computational effort. We also measure with great accuracy $\eta$. As a by-product we are able to determine the fractal dimension $d_H$ of random surfaces at the crumpling transition.