Finite temperature phase diagrams fluctuations

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

This procedure may be a good approximation at zero temperature, but if one considerers finite temperatures this does not hold anymore, since the extension in r-direction is now finite. As a result, there is a region ir/L < A < 7t/At where fluctuations are mainly one-dimensional and purely thermal. This region was disregarded in previous treatments. As we will see, fluctuations from this region have an important influence on the overall phase diagram. 

To summarize all the information gained from the different observables, we construct the approximate boundaries of different regimes in the T-(s plane. The pseudophase diagram is displayed in Fig. 13.12 and the different pseudophases are denoted by the abbreviations introduced in the previous subsections. Transitions between conformational phases are indicated by stripes. It must be noted that their thickness is due to the the different locations of peaks when considering different fluctuating quantities. This is a typical feature of a finite system, where different indicators of transitions (e.g., transition temperatures) do... 

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