Regensburg 2007 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Statistical physics (general)
DY 12.3: Vortrag
Dienstag, 27. März 2007, 10:30–10:45, H3
Nonanalyticities of entropy functions of finite and infinite systems — •Michael Kastner — Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spin-like model which is exactly solvable for both, finite and infinite system sizes, showing a phase transition in the latter case. The microcanonical entropy is found to have exactly one nonanalytic point in the interior of its domain. For all finite system sizes, this point is located at the same fixed energy value εcfinite, jumping discontinuously to a different value εcinfinite in the thermodynamic limit. Remarkably, εcfinite equals the average potential energy of the infinite system at the phase transition point. The result, supplemented with results on nonanalyticities of the microcanonical entropy for other models, indicates that care is required when trying to infer infinite system properties from finite system nonanalyticities.