Abstract
We investigate the influence of spatial correlations between the values of the random field on the critical behavior of random-field lattice models and derive a generalized version of the Schwartz-Soffer inequality for the averages of the susceptibility and its disconnected part. At the critical point this leads to a modification of the Schwartz-Soffer exponent inequality for the critical exponents η and η- describing the divergences of the susceptibility and its disconnected part, respectively. It now reads η- ≤ 2η-2y where 2y describes the divergence of the random-field correlation function in Fourier space. As an example we exactly calculate the susceptibility and its disconnected part for the random-field spherical model. We find that in this case the inequalities actually occur as equalities.
Recommended Citation
T. Vojta and M. Schreiber, "Generalization of the Schwartz-Soffer Inequality for Correlated Random Fields," Physical Review B (Condensed Matter), vol. 52, no. 2, pp. R693 - R695, American Physical Society (APS), Jul 1995.
The definitive version is available at https://doi.org/10.1103/PhysRevB.52.R693
Department(s)
Physics
International Standard Serial Number (ISSN)
0163-1829
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 1995 American Physical Society (APS), All rights reserved.
Publication Date
01 Jul 1995
