Crucial combinations of critical exponents for liquids-vapour and ferromagnetic second-order phase transitions
Faculty of Sciences. Physics

article

2014
London
, 2014

Physics

Chemistry

Physics and chemistry of liquids. - London

52(2014)
:5
, p. 697-699

0031-9104

000341446800010

E

English (eng)

University of Antwerp

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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