Tuesday, July 16, 2013

1307.3987 (Timo Dewenter et al.)

Exact ground states of one-dimensional long-range random-field Ising

Timo Dewenter, Alexander K. Hartmann
We investigate the one-dimensional long-range random-field Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability p ~ 1/r^(1+sigma), where r is the distance between these spins and sigma is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to L = 2^19 via graph theoretical algorithms for four different values of sigma = 0.25, 0.4, 0.5, 1.0 while varying the strength h of the random fields. For each of these values several independent physical observables are calculated, i.e., magnetization, Binder parameter, susceptibility and a specific-heat-like quantity. The ferromagnet-paramagnet transitions at critical values h_c(sigma) as well as the corresponding critical exponents are obtained. The results agree well with theory, but for sigma = 0.5 the critical random-field strength h_c > 0 in contrast to what was expected from analytical studies.
View original: http://arxiv.org/abs/1307.3987

No comments:

Post a Comment