Title
Unified theory of critical exponents generated by the Ising Hamiltonian for discrete dimensionalities 2, 3 and 4 in terms of the critical exponent etaUnified theory of critical exponents generated by the Ising Hamiltonian for discrete dimensionalities 2, 3 and 4 in terms of the critical exponent eta
Author
Faculty/Department
Faculty of Sciences. Physics
Research group
Department of Physics
Publication type
article
Publication
London,
Subject
Physics
Chemistry
Source (journal)
Physics and chemistry of liquids. - London
Volume/pages
54(2016):1, p. 127-129
ISSN
0031-9104
ISI
000365724100011
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We present here a unified theory embracing solely the discrete values d = 2, 3 and 4. The critical exponent. is central of this theory. The basic assumption made is that, for these three discrete values, we can express the critical exponent. in the form 14 + 3d. This formula contains the exact values for d = 2 and 4, namely 7/4 and 1, respectively. For d = 3, this formula yields the value 5/4 obtained earlier by Zhang (Philo. Mag. 87 (2007) 5309) from an analytical theory in which the mathematical difficulties associated with the Ising Hamiltonian were bypassed by two clearly stated conjectures. Earlier, K. G. Wilson (Phys. Rev. Lett. 28 (1972) 548), however, had proposed. = 1.247 from the low-order terms in the 2 -expansion. Kardar's book contains the value. = 1.238 obtained by Borel summation of the epsilon expansion. Thus, the critical exponents given here for d = 2, 3 and 4 in terms of. and of course d itself are either exact or of such an accuracy that experimental error should embrace them.
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