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diff --git a/essential-ising.tex b/essential-ising.tex index cdd7cd6..ea8e9eb 100644 --- a/essential-ising.tex +++ b/essential-ising.tex @@ -374,7 +374,7 @@ correction appears to match data quite well. \end{figure} Abrupt phase transitions, such as the jump in magnetization in the Ising -model below $T_c$, are known to imply essential singularities in the free +model below $T_\c$, are known to imply essential singularities in the free energy that are usually thought to be unobservable in practice. We have argued that this essential singularity controls the universal scaling behavior near continuous phase transitions, and have derived an explicit @@ -384,7 +384,7 @@ for the Ising model in a field, and showed that incorporating our singularity into the scaling function gives good convergence to the simulations in \twodee. Our results should allow improved high-precision functional forms for the free -energy~\cite{CaselleXXX}, and should have implications for the scaling +energy~\cite{caselle.2001.critical}, and should have implications for the scaling of correlation functions~\cite{YJXXX,XXX}. Our methods might be generalized to predict similar singularities in systems where nucleation and metastability are proximate to continuous phase transitions, such as 2D superfluid |