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The Effect of Higher‐Order Cumulants in the Random‐Field Ising Model
Author(s) -
Janiš V.
Publication year - 1986
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221380218
Subject(s) - cumulant , diagrammatic reasoning , statistical physics , scaling , dimension (graph theory) , critical dimension , mathematics , ising model , curse of dimensionality , field (mathematics) , random field , dimensionality reduction , order (exchange) , physics , quantum mechanics , statistics , combinatorics , pure mathematics , computer science , geometry , economics , finance , artificial intelligence , programming language
It is shown that below a critical dimension d c = 4 higher‐order random‐field cumulants contribute to the divergent part of the free energy. They renormalize the standard diagrammatic expansion into the most divergent terms in weak random fields in such a way that the perturbative effective dimensionality in the scaling region of the d < 4 model is two. It is argued that any dimensional reduction based on a diagrammatic expansion is doubtful in lower dimensions.