The new material will be the use of wavelet decompositions to study the Ising model of a magnet, and the sorts of information one can extract from Monte Carlo dynamics simulations via wavelet decompositions. We have just begun writing up our results, so preprints are not available. First, I will introduce wavelet expansions, which are a new mathematical method that may be useful in physics. Wavelets may formally be viewed as extensions of the orthogonal functions familiarly used in physics. Isolated examples of wavelet expansions, such as Haar and Gabor transforms, have long been known.
Wavelets provide complete, sometimes non-orthogonal, sets of basis functions.
Some wavelet expansions can be generated recursively, suggesting computation efficiencies. Other wavelet expansions have compact support, so that, e.g., in a wavelet decomposition of a piece of music, alteration of a single note changes local coefficients without affecting most of the expansion. While there is a large mathematical literature on wavelets, concrete applications of wavelet expansions in the physics literature do not appear to be common. I've got two wavelet probelms for your consideration. Please download and print this file before commenting.