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Refined semi-empirical formula for liquid–vapour critical point exponent δ and its relevance to the random field Ising model

Recent work in D.J. Klein and N.H. March, Phys. Lett. A 372, 5052 (2008) has considered, by a semi-empirical approach, the critical exponent δ at the liquid–vapour critical point as a function of dimensionality D. Here we first refine δ(d′), again semi-empirically, but with better results for other critical exponents, especially η(d′). The resulting form of δ(d′) is then utilised to discuss the random field Ising model. Systems with random fields are expected to exhibit drastically modified critical properties. We discuss the relation between a d-dimensional spin system in a random field with a d′-dimensional spin assembly in a zero magnetic field. A further matter focused in here concerns effective reduced dimensionality and hyperscaling relations. We conclude by assessing the way in which the available experimental results relate to the issues raised above.