# Determination of the Crumpling Fractal Dimension Via k-Space MCRG

## TL;DR

This paper uses momentum space MCRG to estimate the fractal dimension at the crumpling transition in triangulated surfaces, providing tentative critical exponent values and insights into the transition's nature.

## Contribution

It applies momentum space MCRG to determine critical exponents and fractal dimensions at the crumpling transition, a novel approach in this context.

## Key findings

- Estimated critical exponent η between -1.0 and -1.3
- Fractal Hausdorff dimension between 3 and 4
- Results suggest a specific universality class for the transition

## Abstract

Motivated by the successful application of MCRG in momentum space to $\lambda \phi^4_3$ we determine the critical exponents at the crumpling transition in fixed triangulated surfaces. The results are still tentative, but suggest that $-1.0\ge \eta \ge -1.3$, pointing at a value for the fractal Hausdorff dimension at the crumpling transistion fixed point somewhere between 3 and 4.