Two dimensional inhomogeneous classical systems at criticality

What the math gives to ML

The paper provides a constructive mechanism for preserving critical, scale-free behavior under slowly varying couplings: inhomogeneous lattice systems are described at long distances by a conformal field theory in a curved metric. For the six-vertex model, integrability and the interaction structure are retained by enforcing a site-independent anisotropy parameter while allowing local weights to vary through spectral parameters. A transferable neural-network design is a two-dimensional residual or recurrent lattice whose local mixing coefficients vary spatially but satisfy the same invariant, with a learned metric controlling propagation speed and a predicted transition between fluctuating and frozen regions.