Random Ising model in three dimensions: theory, experiment and simulation - a difficult coexistence

TL;DR

This paper reviews theoretical, experimental, and simulation methods for studying disorder in the 3D Ising model, highlighting discrepancies and challenges in achieving consistent results across approaches.

Contribution

It provides a comparative analysis of different methods for investigating disorder effects in the 3D Ising model, emphasizing the complexities in reconciling their findings.

Findings

Renormalisation group calculations are quite accurate.

Experimental measurements of critical exponents are highly precise.

Monte Carlo simulations aim for comparable accuracy but face challenges.

Abstract

We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation group calculations provide quite accurate results. Experiments carried out on crystalline mixtures of compounds lead to measurements as accurate as three digits on the values of critical exponents. Numerically, extensive Monte Carlo simulations then pretend to be of comparable accuracy. Life becomes complicated when details are compared between the three approaches.