This main aim of this is to nvestigate the 3-dimensional Ising model and similar spin models on very large lattices, using parallel algorithms developed by the applicants. Our current code makes it possible to simulate systems which are several orders of magnitude larger than those used in the existing literature. We have already set a world record using system sizes with more than 10^12 spins in total, corresponding to lattices with side over 10.000. Additionally we will investigate spin systems in dimension four which are relevant for the study of quantum field theories, and some disordered spin systems which are challenging for smaller sizes as well.
Using data from these large systems we will investigate the properties at the critical point of the system. In particular we will give new estimates for the critical exponents of these models. Critical exponents have for a long time been assumed to have the same value above and below the critical point, but earlier work with systems of size up to side 512, for the Ising model, have shown that there is no clear support for this assumption, and that systems with side less than 200 are too far from the asymptotic behaviour to give reliable data.
Using these much larger systems we can give better estimates of the high adn low temperature behaviour of the exponents, and so also test whether they are the same or not. If the latter turns out to be the case it would represent a breakdown of one of the major theoretical assumptions about critical points in three dimensions. Using high resolution data for smaller systems we can also characterize the scaling limits of these models, and through that also find properties of the related quantum field theories.