Geometrical Properties of Two-Dimensional Interacting Self-Avoiding Walks at the Theta-Point

TL;DR

This study uses Monte Carlo simulations to analyze the geometrical properties of two-dimensional interacting self-avoiding walks at the theta point, confirming theoretical predictions and providing detailed geometric measurements.

Contribution

It provides the first detailed Monte Carlo analysis of the geometrical features of 2D interacting self-avoiding walks at the theta point, verifying theoretical predictions.

Findings

Confirmed Coulomb-gas predicted critical exponents.

Determined the theta-point temperature as 1.4986(11).

Analyzed shape ratios, asphericity, and end-to-end distribution, matching theoretical behaviors.

Abstract

We perform a Monte Carlo simulation of two-dimensional N-step interacting self-avoiding walks at the theta point, with lengths up to N=3200. We compute the critical exponents, verifying the Coulomb-gas predictions, the theta-point temperature T_theta = 1.4986(11), and several invariant size ratios. Then, we focus on the geometrical features of the walks, computing the instantaneous shape ratios, the average asphericity, and the end-to-end distribution function. For the latter quantity, we verify in detail the theoretical predictions for its small- and large-distance behavior.