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-
-The renormalization group and the scaling theories that result from its use
-have become essential to our understanding of singular behavior in
-thermodynamic functions at continuous phase transitions. Despite this, they
-have long been viewed as irrelevant to the quantitative study of abrupt phase
-transitions, and likewise the presence of an abrupt phase transition has
-typically been considered irrelevant to scaling analysis. Our work
-demonstrates, for one common model with both a continuous and a
-line of abrupt transitions, that well-known singularities in thermodynamic
-functions at the abrupt transition long assumed to be unobservable are in fact
-part of the scaling theory of the critical point, and make explicit
-predictions confirmed by numerics. This result indicates that many published
-statistical models whose abrupt transitions were not incorporated into scaling
-theories should be revisited, and introduces a novel new method for
-determining new universal scaling properties in previously poorly-understood
-regimes.
-
-