A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.
Bibliographical noteThe final publication is available at Springer via http://dx.doi.org/10.1007/s10955-018-1955-7
- Random field Ising models
- Universality class
- Optimization methods
Fytas, N., Martin-Mayor, V., Picco, M., & Sourlas, N. (2018). Review of Recent Developments in the Random-Field Ising Model. Journal of Statistical Physics, 172, 665 - 672. https://doi.org/10.1007/s10955-018-1955-7