Systematic classification of transitions by inflection-point analysis

3 Systematic classification of transitions by inflection-point analysis 

To make it applicable to other transition types as well, it is attractive to extend this flatness idea by replacing the Maxwell construction with a more general principle, the principle of least sensitivity. This is a weaker condition, but it allows us to investigate first-and higher-order transitions by a microcanonical analysis more systematically and in much more detail [61], 

In this scheme, a transition between phases is defined to be offirst order if the slope of the corresponding inflection point of fi(E) atE = Etr is positive. 

In the case where the inflection point has a negative slope, the phases caimot coexist and the latent heat is zero, Ag=0. In complete analogy to phase transitions in the thermodynamic limit, such transitions are classified as of second order. 

Inflection-point analysis ot the inverse temperature fi (f) and its derivative y (f) as tunctions otenergy E tor a system exhibiting a first- and a second-order transition, the maxima ot y (E) indicate transitions between the phases A and B at 4 and B and C at E. The associated points (Eff) = pff and P(E ) = define the transition temperatures Tff = and According to the classification scheme otinflection-point 

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