Ideal chains with fixed self-intersection rate

TL;DR

This paper studies ideal lattice chains with a fixed self-intersection ratio, revealing a collapse transition at a critical value, with behaviors resembling self-avoiding walks and globule formations, akin to thermodynamic coil-globule transitions.

Contribution

It introduces a model of ideal chains with a fixed self-intersection rate and analyzes its phase transition and structural properties.

Findings

Identifies a collapse transition at a critical self-intersection rate

Shows different structural regimes: self-avoiding walk-like and compact globules

Reveals similarities to thermodynamic coil-globule transition phenomena

Abstract

We consider ideal chains in a hypercubic lattice \mathbb{Z}^{d}, d\geq3, with a fixed ratio m of self-intersection per monomer. Despite the simplicity of the geometrical constraint, this model shows some interesting properties, such as a collapse transition for a critical value m_{c}. Numerical simulations show a Self-Avoiding-Walk-like behavior for m<m_{c}, and a compact cluster configuration for m>m_{c}. The collapse seems to show the same characteristics as the canonical thermodynamical models for the coil-globule transition.