Corrections to Scaling in Random Resistor Networks and Diluted Continuous Spin Models near the Percolation Threshold

TL;DR

This paper analyzes how irrelevant operators cause corrections to scaling in random resistor networks and continuous spin models near the percolation threshold, revealing inaccuracies in previous results.

Contribution

It identifies and calculates corrections to scaling from irrelevant operators, accounting for operator mixing, and corrects prior incomplete or incorrect findings.

Findings

Corrections to scaling are influenced by irrelevant operators in these systems.

Previous results on corrections to scaling were found to be incorrect or incomplete.

Operator mixing under renormalization significantly affects the corrections to scaling.

Abstract

We investigate corrections to scaling induced by irrelevant operators in randomly diluted systems near the percolation threshold. The specific systems that we consider are the random resistor network and a class of continuous spin systems, such as the x-y-model. We focus on a family of least irrelevant operators and determine the corrections to scaling that originate from this family. Our field theoretic analysis carefully takes into account, that irrelevant operators mix under renormalization. It turns out that long standing results on corrections to scaling are respectively incorrect (random resistor networks) or incomplete (continuous spin systems).