# The flat phase of fixed-connectivity membranes

## TL;DR

This paper reviews the theoretical understanding of the flat phase in fixed-connectivity membranes and presents Monte Carlo simulation results confirming long-range order and critical exponents, aligning with theoretical predictions.

## Contribution

It provides the first large-scale Monte Carlo simulation of fixed-connectivity membranes, verifying long-range order and critical exponents in the flat phase.

## Key findings

- Confirmation of long-range order in the flat phase
- Determination of critical exponents
- Comparison with theoretical models

## Abstract

The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system \cite{BCFTA}. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.