This project will investigate the 3-dimensional Ising model on lattices using a new parallel algorithm developed by the applicants. This code will make it possible to simulate systems which are several orders of magnitude larger than those used in the existing literature. In particular we expect to 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 and five, which hare relevant for the study of quantum field theories, as well.
Using data from these large system we intend to investigate the properties at the critical point of the system In particular we will give new estimates for the critical exponents of the model. These 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 have shown that there is no clear support for this assumption, and that systems with side less than 200 are too from the asymptotic behaviour to give reliable data.
Using these much larger systems we expect to be able to give a clear answer to whether the high an low temperature behaviour of the exponents at the critical point 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. We also expect to be able to rule out some existing conjectures regarding the value of some of the critical exponents and the value of the critical temperature of the model.