# Numerical simulation of random paths with a curvature dependent action

## TL;DR

This paper investigates the behavior of closed random paths in three-dimensional space with a focus on how curvature influences their properties, revealing complexities in numerical simulations despite existing theoretical predictions.

## Contribution

It provides a high-statistics numerical analysis of curvature-dependent random paths, highlighting challenges in interpreting results without comprehensive theoretical backing.

## Key findings

- No crumpling transition observed at finite curvature coupling
- Two regimes in specific heat separated by a smooth transition
- Highlights difficulties in numerical analysis without theoretical guidance

## Abstract

We study an ensemble of closed random paths, embedded in R^3, with a curvature dependent action. Previous analytical results indicate that there is no crumpling transition for any finite value of the curvature coupling. Nevertheless, in a high statistics numerical simulation, we observe two different regimes for the specific heat separated by a rather smooth structure. The analysis of this fact warns us about the difficulties in the interpretation of numerical results obtained in cases where theoretical results are absent and a high statistics simulation is unreachable. This may be the case of random surfaces.