Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension

Details Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension Critical behavior of the Random-Field Ising model at and beyond the Upper Critical Dimension

2010-10-14

arxiv.org/abs/1010.2911v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages and 13 figures; A consise summary of this work can be found in the papercore database at http://www.papercore.org/Ahre

Scientific paper

The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility and of the correlation length. For dimensions d=6,7 which are larger or equal to the assumed upper critical dimension, d_u=6, mean-field behaviour is found, i.e. alpha=0, beta=1/2, gamma=1, nu=1/2. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.

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