  I revisit the problem of a charged particle on a two-dimensional lattice
immersed in a constant (electro)magnetic field, and discuss the energy spectrum
- Hofstadter's butterfly - from a new, quantum field theoretical perspective.
In particular, I point out that there is an intricate interplay between a) the
structure of the butterfly at low magnetic flux, b) the absence of asymptotic
freedom in QED and c) the enhancement of the quark condensate by a magnetic
field at zero temperature. I proceed to discuss the response of the QCD
condensate to the magnetic field at nonzero temperatures in four space-time
dimensions, present the resulting phase diagram and compare it to low-energy
model predictions.
