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.

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.

Included in

Physics Commons

Share

 
COinS