Synergistic development of differential approximants and the finite lattice method in lattice statisticsIn honour of the 70th birthday for Professor A J Guttmann

Several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena. These studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of d...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 50; no. 17
Main Author Enting, I G
Format Journal Article
LanguageEnglish
Published IOP Publishing 24.03.2017
Subjects
critical exponents
lattice statistics
series analysis
series expansions
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Summary:Several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena. These studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of differential approximants in analysing such series. One of these strands of research ultimately led to the result that a number of unsolved lattice statistics problems cannot be expressed as D-finite functions. Somewhat ironically, given power and success of differential approximants in analysing series, neither the assumed functional form, nor any finite generalisation thereof can fit such cases exactly.
Bibliography:JPhysA-107059.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aa6202