[yummypaint]

I reccommend also doing some reading about foundational lattice field theory concepts in parallel with classic QFT. Comparing and contrasting the two can help with understanding both. Maybe start with ultraviolet divergence? Lattice based theories have also been more successful as far as making good predictions. I think it appeals to intuition that people who write software may find more familiar.

[jiggawatts]

I've looked, but generally I found that lattice models:

1) Have dramatic simplifications, such as 2D models.

2) Use made-up physical constants to make the computations tractable, e.g.: arbitrary fermion masses and properties.

3) Are based on some sort of global minimisation as the core computation, which isn't a local function. It's solving physics differential equations numerically, sure, but not in the same "local way" that the Universe does.

4) Outputs some simple scalar value or 1D graph as the result. I've only seen a small handful of codes that can output a "picture", as in a rendering of some aspect of a volumetric field.

5) Can't model most aspects of QM and/or SR due to the corner-cutting somewhere.

Probably the best extant codes are the ones used for electromagnetic simulations for radar or radiofrequency systems. Due to the long (macroscopic) wavelengths, these inherently required a QED-style treatment. Similarly, correctly handling things like doppler shifts requires SR.

[yummypaint]

The simplifications facilitated by lattice techniques are one of the main features. The non-perturbative nature of QCD makes it impossible to do many calculations that would be trivial in QED. As two strongly interacting particles are separated, the strength of their interaction increases, which is the opposite of everything else we're used to. In QED, you can often safely consider the first few feynman diagrams to be a good approximation of the whole process. In QCD, infinitely many feynman diagrams contribute non-negligibly to the result, which is why traditional methods fail. Here is an example of lattice methods applied to nuclear properties: https://www.frontiersin.org/articles/10.3389/fphy.2020.00174...