Critical scaling in random-field systems: 2 or 3 independent exponents?
1 LPTMC, CNRS- UMR 7600, Université Pierre et Marie Curie - boîte 121, 4 Pl. Jussieu, 75252 Paris cédex 05, France, EU
2 Institute of Physics - P.O. Box 304, Bijenička cesta 46, HR-10001 Zagreb, Croatia
Received: 15 April 2013
Accepted: 18 September 2013
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 domain of the d-dimensional random-field O(N) model (RFO(N)M) 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 in d = 3 and d = 4, so that the issue cannot be decided only on the basis of numerical simulations in these spatial dimensions.
PACS: 11.10.Hi – Renormalization group evolution of parameters / 75.40.Cx – Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)
© EPLA, 2013