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

• Published in: Europhysics letters Vol. 103; no. 6; pp. 61001 - 61006
• Main Authors: Tarjus, Gilles, Balog, Ivan, Tissier, Matthieu
• Format: Journal Article
• Language: English
• Published: EDP Sciences, IOP Publishing and Società Italiana di Fisica 01.09.2013
• Subjects: 11.10.Hi; 75.40.Cx
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/103/61001

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.