Wavevector-dependent susceptibility in quasiperiodic Ising models

Using the various functional relations for correlation functions in planar Ising models, new results are obtained for the correlation functions and th e q-dependent susceptibility fbr Ising models on a quadratic lattice with q uasiperiodic coupling constants. The effects are dearest if the interaction s are both attractive and repulsive according to a quasiperiodic pattern. I n particular, an tract scaling limit result for the two-point correlation f unction of the Z-invariant inhomogeneous Ising model is presented and the q -dependent susceptibility is calculated for some cases where the coupling c onstants vary according to Fibonacci rules. It is found that the ferromagne tic case differs drastically From the case with both ferro- and antiferroma gnetic bonds. In the mixed case, the peaks of the q-dependent susceptibilit y are everywhere dense for temperature T both above or below the critical t emperature T,, but due to overlap only a finite number of peaks is visible. This number of visible peaks decreases as T moves away from T,. In the fer romagnetic case, there is typically only one single peak at q = 0, in spite of the aperiodicity present in the lattice. These results provide evidence that in real systems, even if the atoms arrange themselves aperiodically, there will be no dramatic difference in the diffraction pattern, unless the pair correlation function has clear aperiodic oscillations. The number of oscillations per correlation length determines the number of visible peaks.