TY - JOUR
T1 - Restoration of dimensional reduction in the random-field Ising model at five dimensions
AU - Fytas, Nikolaos
AU - Martin-Mayor, Victor
AU - Picco, Marco
AU - Sourlas, Nicolas
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PY - 2017/4/10
Y1 - 2017/4/10
N2 - 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 phenomenon.We close our contribution by comparing universal quantities for the random-field problem at dimensions 3
2\leq D < 6 to their values in the pure Ising model at D − 2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.
AB - 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 phenomenon.We close our contribution by comparing universal quantities for the random-field problem at dimensions 3
2\leq D < 6 to their values in the pure Ising model at D − 2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.
U2 - 10.1103/PhysRevE.95.042117
DO - 10.1103/PhysRevE.95.042117
M3 - Article
SN - 1539-3755
VL - 95
JO - Physical review E: Statistical, Nonlinear, and Soft Matter Physics
JF - Physical review E: Statistical, Nonlinear, and Soft Matter Physics
M1 - 042117
ER -