Surface critical behaviour of the vertex-interacting self-avoiding walk on the square lattice

TL;DR

This paper investigates the surface critical behavior of vertex-interacting self-avoiding walks on a square lattice, revealing new insights into phase transitions and critical exponents through advanced computational methods.

Contribution

It introduces an extended transfer matrix approach combined with DMRG and finite-size scaling to analyze surface critical phenomena and challenges existing conjectures on bulk exponents.

Findings

Critical exponents at ordinary and special points are characterized.

Results for bulk exponents differ from previously conjectured exact values.

Surface critical behavior along the collapse transition line is elucidated.

Abstract

The phase diagram and surface critical behaviour of the vertex-interacting self-avoiding walk are examined using transfer matrix methods extended using DMRG and coupled with finite-size scaling. Particular attention is paid to the critical exponents at the ordinary and special points along the collapse transition line. The question of the bulk exponents ($\nu$ and $\gamma$) is addressed, and the results found are at variance with previously conjectured exact values.