Restoration of dimensional reduction in the random-field Ising model at five dimensions

Physical Review. E
Nikolaos G FytasNicolas Sourlas

Abstract

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomeno...Continue Reading

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Jun 18, 2016·Physical Review Letters·Nikolaos G FytasNicolas Sourlas

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Citations

Jul 20, 2019·Physical Review Letters·Nikolaos G FytasNicolas Sourlas
May 16, 2018·Physical Review. E·N G FytasA Malakis
May 10, 2020·Polymers·Róbinson J Acosta DiazNami F Svaiter
Sep 19, 2020·Physical Review. E·Svetislav MijatovićDjordje Spasojević
Jan 21, 2021·Physical Review. E·Erol VatanseverNikolaos G Fytas
Jan 21, 2021·Physical Review. E·Ivan BalogMatthieu Tissier
Apr 18, 2021·Physical Review. E·Svetislav MijatovićDjordje Spasojević
Jul 18, 2021·Physical Review. E·Dragutin JovkovićDjordje Spasojević
Jul 18, 2021·Physical Review. E·Stefan GraovacDjordje Spasojević

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