The correction-to-scaling exponent in dilute systems

TL;DR

This paper calculates the correction-to-scaling exponent in the 3D dilute Ising model using field theory, achieving good agreement with Monte Carlo results, but finds limitations in the epsilon expansion approach.

Contribution

It provides a field theoretic calculation of the correction-to-scaling exponent for the 3D dilute Ising model, aligning with recent Monte Carlo data.

Findings

Excellent agreement with Monte Carlo calculations

Epsilon expansion does not reliably estimate the exponent in 3D

Field theory methods effectively determine correction-to-scaling exponents

Abstract

The leading correction-to-scaling exponent $\omega$ for the three-dimensional dilute Ising model is calculated in the framework of the field theoretic renormalization group approach. Both in the minimal subtraction scheme as well as in the massive field theory (resummed four loop expansion) excellent agreement with recent Monte Carlo calculations [Ballesteros H G, et al Phys. Rev. B 58, 2740 (1998)] is achieved. The expression of $\omega$ as series in a $\sqrt{\epsilon}$-expansion up to ${\cal O}(\epsilon^2)$ does not allow a reliable estimate for $d=3$.