An Effective Model for Crumpling in Two Dimensions?

TL;DR

This paper explores the crumpling transition in two-dimensional surfaces using a modified model with long-range antiferromagnetic interactions, comparing it to standard models through Monte Carlo simulations to understand phase transition nature.

Contribution

It introduces an effective model replacing disorder effects with long-range interactions and compares its results to standard models for the first time.

Findings

The effective model exhibits a different phase transition behavior.

Monte Carlo simulations reveal the impact of long-range interactions.

Comparison suggests new insights into crumpling phenomena.

Abstract

We investigate the crumpling transition for a dynamically triangulated random surface embedded in two dimensions using an effective model in which the disordering effect of the $X$ variables on the correlations of the normals is replaced by a long-range ``antiferromagnetic'' term. We compare the results from a Monte Carlo simulation with those obtained for the standard action which retains the $X$'s and discuss the nature of the phase transition.