Interface in an Ising model with a spatially varying coupling constant

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Abstract
We consider the Ising model on square and simple-cubic lattices with a nearest-neighbor coupling constant which varies linearly with position in one direction. In the region where the coupling constant K passes through its critical value there is an interface which separates two regions. In one region K is less than its critical value, and the system is essentially in the disordered phase, while in the other region the system is in an ordered phase. We study the properties of this interface, using both mean-field theory and Monte Carlo simulations. In particular, we investigate simple scaling predictions for the behavior of various quantities near the interface. We are also able to obtain good numerical estimates for the exponent combinations β/(1+ν) and ν(1-η)/(1+ν). .AE