Crucial combinations of critical exponents for liquids–vapour and ferromagnetic second-order phase transitions
Norman Henry March
Four combinations of critical exponents pertaining to the Ising model are constructed which yield simply the dimensionality d. One of these, connecting γ and η, is shown to lead to an immediately useful estimates of the sum α + η 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 α = 0 and η = 1/8. But the pioneering work of Wilson based on renormalisation group theory gave the estimate η = 0.037, while the Perk advocates α = 0.1, without however, proceeding a proof. We therefore finally stress the current importance of further experimental measurements. The critical exponent δ 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 η quoted above.
Physics and Chemistry of Liquids•Apr 24, 2014•7 citations