Adsorption of neighbor-avoiding walks on the simple cubic lattice

TL;DR

This study explores neighbor-avoiding walks on a cubic lattice near an adsorbing surface, determining critical behavior and adsorption transition properties, and finds that the adsorption exponent aligns with non-interacting walks but differs from mean-field predictions.

Contribution

It provides the first Monte Carlo analysis of neighbor-avoiding walks' adsorption transition, establishing their critical parameters and universality class in three dimensions.

Findings

Critical temperature T_a=3.274(9)

Crossover exponent φ=0.482(13)

Exponent consistent with self-avoiding walks

Abstract

We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous results using self-avoiding walks and self-avoiding trails. The connection is that neighbor-avoiding walks are equivalent to the infinitely repulsive limit of self-avoiding walks with monomer-monomer interactions. Such repulsive interactions can be seen to enhance the excluded volume effect. We calculate the critical behavior of the adsorption transition for neighbor-avoiding walks, finding a critical temperature $T_{\text a}=3.274(9)$ and a crossover exponent $\phi=0.482(13)$, which is consistent with the exponent for self-avoiding walks and trails, leading to an overall combined estimate for three dimensions of $\phi_\text{3D}=0.484(7)$. While questions of universality have previously been raised regarding the value of adsorption exponents in three dimensions, our results indicate that the value of $\phi$ in the strongly repulsive regime does not differ from its non-interacting value. However, it is clearly different from the mean-field value of $1/2$ and therefore not super-universal.