I am writing this post to inquire if any progress has been made in solving problem 8B (Proof of Universality) proposed by Barry Simon in 1984.
The problem goes like this:
Show that the critical exponents in the three-dimensional Ising models with nearest neighbor coupling but different bond strengths in the three directions are independent of the ratios of these bond strengths.
Thnx!
An update from 2004 is given by Yurishchev in Universality in the partially anisotropic three-dimensional Ising lattice.
When the lattice anisotropy parameter is varied by three orders of magnitude, the numerically estimated thermal and magnetic critical exponents change only by a few per cent, in accord with the universality hypothesis.
No progress has been made on a mathematically rigorous calculation. Such progress is expected to be as challenging as an exact solution of the 3D Ising model, which has been elusive.
