Critical exponents of four-dimensional random-field Ising systems

Details Critical exponents of four-dimensional random-field Ising systems Critical exponents of four-dimensional random-field Ising systems

2002-01-24

arxiv.org/abs/cond-mat/0201441v1

Phys. Rev. B 65, 174427 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 10 figures, 1 table, revtex4

Scientific paper

10.1103/PhysRevB.65.174427

The ferromagnet-to-paramagnet transition of the four-dimensional random-field Ising model with Gaussian distribution of the random fields is studied. Exact ground states of systems with sizes up to 32^4 are obtained using graph theoretical algorithms. The magnetization, the disconnected susceptibility, the susceptibility and a specific heat-like quantity are calculated. Using finite-size scaling techniques, the corresponding critical exponents are obtained: \beta=0.15(6), \gamma`=3.12(10), \gamma=1.57(10) and \alpha=0 (logarithmic divergence). Furthermore, values for the critical randomness h_c=4.18(1) and the correlation-length exponent \nu=0.78(10) were found. These independently obtained exponents are compatible with all (hyper-) scaling relations and support the two-exponent scenario (\gamma`=2\gamma)

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