We propose a new empirical procedure for detecting phase transition from a single sample of a Gibbs-Markov random field. The method is based on frequencies for large deviations when the whole sample is divided in smaller blocks and estimates for the rate function. We relate our approach to an almost sure large deviation principle.
"Detecting phase transition for Gibbs measures." Ann. Appl. Probab. 7 (2) 545 - 563, May 1997. https://doi.org/10.1214/aoap/1034625344