Phase transitions of the variety of random-field Potts models

The phase transitions of random-field q-state Potts models in d=3 dimensions are studied by renormalization-group theory exact solution a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions cubic lattice. recursion, under rescaling, coupled and random-bond (induced rescaling random fields) probability distributions is followed to obtain diagrams. Unlike the Ising model (q=2), several types fields can be defined for q >= 3 models, including random-axis favored, disfavored, randomly favored or disfavored cases, all which studied. Quantitatively very similar diagrams obtained, given three field randomness, with low-temperature ordered persisting, increasingly as temperature lowered, up threshold d=3, calculated temperatures below zero-field critical temperature. Phase thus obtained compared function $q$. low-q reaches higher temperatures, while high-q it fields. This calculation result physically explained.