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Review of Recent Developments in the Random-Field Ising Model

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Abstract

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.

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Acknowledgements

We would like to thank Giorgio Parisi for his hospitality in Rome, where part of this work has been completed. V.M.-M. was partially supported by MINECO (Spain) through Grant No. FIS2015-65078- C2-1-P (this contract partially funded by FEDER). N.G.F. and M.P. acknowledge support by the Royal Society’s International Exchange Scheme 2016/R1.

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Authors and Affiliations

  1. Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK

    Nikolaos G. Fytas

  2. Departamento de Física Téorica I, Universidad Complutense, 28040, Madrid, Spain

    Víctor Martín-Mayor

  3. Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), 50009, Saragossa, Spain

    Víctor Martín-Mayor

  4. Sorbonne Universités, Université Pierre et Marie Curie - Paris VI, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, 75252, Paris Cedex 05, France

    Marco Picco

  5. Laboratoire de Physique Théorique de l’ENS, École Normale Supérieure, PSL Research University, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005, Paris, France

    Nicolas Sourlas

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  1. Nikolaos G. Fytas
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  2. Víctor Martín-Mayor
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  3. Marco Picco
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  4. Nicolas Sourlas
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Correspondence to Nicolas Sourlas.

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Fytas, N.G., Martín-Mayor, V., Picco, M. et al. Review of Recent Developments in the Random-Field Ising Model. J Stat Phys 172, 665–672 (2018). https://doi.org/10.1007/s10955-018-1955-7

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  • DOI: https://doi.org/10.1007/s10955-018-1955-7

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