Title
Crucial combinations of critical exponents for liquids-vapour and ferromagnetic second-order phase transitions
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
London ,
Subject
Physics
Chemistry
Source (journal)
Physics and chemistry of liquids. - London
Volume/pages
52(2014) :5 , p. 697-699
ISSN
0031-9104
ISI
000341446800010
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Four combinations of critical exponents pertaining to the Ising model are constructed which yield simply the dimensionality d. One of these, connecting. gamma and eta, is shown to lead to an immediately useful estimates of the sum a + eta in three dimensions, about which exponents controversy still exists. This sum in three dimensions is shown to be very near or equal to 1/8, a condition which Zhang's predictions, for the exact solution of the 3D Ising model, satisfy with alpha = 0 and eta= 1/8. But the pioneering work of Wilson based on renormalisation group theory gave the estimate eta = 0.037, while the Perk advocates alpha = 0.1, without however, proceeding a proof. We therefore finally stress the current importance of further experimental measurements. The critical exponent d may be the most favourable focus, to distinguish between Zhang's prediction of 13/3 and a value around 4.8 following for d = 3 from Wilson's value of eta quoted above.
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