Critical behaviour of inhomogeneous lattices

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Abstract
Large-scale inhomogeneities in magnetic lattices are found to reduce the sharpness of the critical singularities, the changes in the critical indices being the same for all properties. They also cause the lattice to have at least two critical temperatures. For a typical three-dimensional Ising lattice of this type the specific heat and its slope remain finite at all temperatures. On the other hand, if the inhomogeneities are small scale and randomly distributed it is shown by rigorous analysis of some examples (certain excluded volume, percolation, Gaussian and Ising lattice problems) that the critical indices still have the usual cyclic lattice values. Hence it is suggested that random impurities are not responsible for the rounding of specific-heat curves observed experimentally.

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