Microcanonical interpretation The backbending effect

We introduced the microcanonical analysis in Section 2.7 and found that the density of states g E) already contains all relevant information about the phases of the system. Alternatively, one can also use the phase space volume AG(E) of the energetic shell that represents the macrostate in the microcanonical ensemble in the energetic interval (E,E+ AE) with AE being sufficiently small to satisfy AG E)=g E)AE. In the limit AE — 0, the total phase space volume up to the energy E can thus be expressed as G E) = dE g(E ). Since g E) is positive for all E, G(E) is a monotonically increasing function and this quantity is suitably related to the microcanonical entropy S(E) of the system. In the definition of Hertz, 

As long as the mapping between the caloric temperature T and the system energy E is bijective, the canonical analysis of crossover and phase transitions is suitable since the temperature can be treated as external control parameter. For systems where this condition 

Microcanonical specific heat Cy (f) for the 2 x FI complex. Note the negativity in the backbending regions. From [254]. 

The inverse caloric temperature T (E) is also plotted in Fig. 11.5. For a fixed temperature in the interval T (7 se0.169 and 0.231), different energetic 

Logarithmic plots of the canonical energy histograms (not normalized) at f 0.18 and T 020, respectively. 

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