I will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. I will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, I will then show how one can define a "lowest Landau level" in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.

Nonzero Temperature and Density