The Site-Diluted Ising Model in Four Dimension

TL;DR

This paper clarifies the critical scaling behavior of the four-dimensional random-site Ising model by completing existing predictions with logarithmic corrections and confirming them through numerical analysis.

Contribution

It completes the set of analytic predictions for the model's scaling behavior and verifies these predictions numerically, resolving previous fragmentation.

Findings

Confirmed the leading scaling behavior with numerical methods

Discriminated between different analytic predictions at the level of logarithmic corrections

Provided a unified scaling picture for the model

Abstract

In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.