Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions

TL;DR

This paper investigates the scaling behavior of the two-dimensional site-diluted Ising model, focusing on magnetic and thermal sectors, and confirms the validity of scaling hypotheses and logarithmic correction relations through numerical and theoretical analysis.

Contribution

It provides a detailed analysis of the model's scaling behavior, especially the Lee-Yang zeros, and supports the strong scaling hypothesis with high-accuracy data.

Findings

High-precision determination of Lee-Yang zeros

Confirmation of scaling relations for logarithmic corrections

Insights into the specific heat and its corrections

Abstract

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.