Critical exponents proposed for marginal Fermi liquid

Abstract

Iqbal, Liu and Mezei (ILM) [1] have proposed critical exponents α, β and δ in terms of a quantity νILM, which gives marginal Fermi liquid behaviour when νILM = 1/2. In particular, this value reproduces in the normal state of high T c cuprates, the electrical resistivity proportional to temperature (T) over a wide range of T, as found experimentally. A consequence shown here is that Griffiths' inequality becomes an equality for all νILM, while Josephson's inequality is also satisfied for all positive values of νILM. The choice νILM = 1/4, on the other hand, reproduces the mean field values of α, β and δ. We propose a specific relation between δ and η for the Ising model by using the ILM family as a guideline.