When did "scale invariance" started to be seen as an important concept in the theory of phase transition?
Phase transition and critical points started to be investigated in earnest in the middle of the 19th century, with the study of critical opalescence (Andrew/Faraday) : at the critical point of a liquid, the liquid start to get cloudy/diffuse, a phenomenon widely attributed to the scale invariance of the medium nowadays. I like to pinpoint when scale invariance was first observed, and when it started to be seen as something important in the theory of phase transition.
It seems that a lot of what was needed to introduce scale invariance in physics was already here at the start of the 19th century, with brownian motion and fractals being investigated. Marian Smoluchowski was the first (at the beginning of the 20th century) to guess that opalescence was due to large fluctuations in the fluid (but that's not "scale invariance").
Conformal invariance (a generalisation of scale invariance), started to get applied to phase transition in the 70's. So that's an upper boundary I guess. A google ngram seems to indicate that "scale invariance" only became a thing when conformal invariance started. But one of A. Migdal anecdote seems to indicate that scale invariance was already seen as "old news" in the beginning of the 70's (pdf, page 34-35).
Sorry if the "history of science" question is out of bounds for this stackexchange.