Statistics of self-avoiding walks on randomly diluted lattice

TL;DR

This paper presents a detailed numerical analysis of self-avoiding walks on randomly diluted lattices, focusing on critical exponents across different conditions, revealing new properties and refining previous understanding.

Contribution

It provides the first comprehensive numerical calculation of critical exponents for SAWs on diluted lattices in multiple dimensions, exploring various disorder configurations and weighting schemes.

Findings

Calculated critical exponents $ u$ and $ au$ for different occupation probabilities

Identified new properties and subtleties in the exponents' definitions

Compared results with previous studies to refine existing knowledge

Abstract

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.