1304.4146 (Gilles Tarjus et al.)

Critical scaling in random-field systems: 2 or 3 independent exponents?    [PDF]

Gilles Tarjus, Ivan Balog, Matthieu Tissier

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole (d,N) domain of the d-dimensional random-field O(N) model and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random field Ising model are extremely close to the predictions of the two-exponent scaling, so that the issue cannot be decided on the basis of numerical simulations.

View original: http://arxiv.org/abs/1304.4146