Lattice-lattice scaling and the generalized law of corresponding states

Abstract

Lattice-dependent scaled temperature and field variables are shown to produce a generalization of the law of corresponding states. This generalization equates the appropriately scaled free energy of a system on different lattices in the critical region. The theory is tested by making use of the results of series analysis-in particular the critical amplitudes-for the Ising, XY and Heisenberg models, as well as the exact results known for the spherical model. The theory is found to be consistent with all the available data. The scaled field variable appears to be model independent, depending only on the underlying lattice, while the scaled temperature variable is found to be model dependent. I..