# Adsorption of interacting self-avoiding trails in two dimensions

## TL;DR

This study explores how interacting self-avoiding trails in two dimensions adsorb onto a boundary, revealing phase transitions and universality properties, with particular focus on the special adsorption point and its scaling behavior.

## Contribution

It provides the first detailed simulation analysis of adsorption transitions of interacting trails, highlighting non-universality at the special adsorption point due to scaling corrections.

## Key findings

- Confirmed phase diagram with swollen, collapsed, and adsorbed phases.
- Established universality of normal adsorption transition at low bulk interaction.
- Observed non-universality at the special adsorption point, likely due to scaling corrections.

## Abstract

We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a collapse transition of the trails from a swollen to a collapsed phase, separated by a critical state. If the trail is in the critical state, the universality class of the adsorption transition changes; this is known as the special adsorption point. Using flatPERM, a stochastic growth Monte Carlo algorithm, we simulate the adsorption of self-avoiding interacting trails on the square lattice using three different boundary scenarios which differ with respect to the orientation of the boundary and the type of surface interaction. We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed phases in all three scenarios, and confirm universality of the normal adsorption transition at low values of the bulk interaction strength. Intriguingly, we cannot confirm universality of the special adsorption transition. We find different values for the exponents; the most likely explanation is that this is due to the presence of strong corrections to scaling at this point.