Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-05-16
Phys. Rev. Lett. 97, 100602 (2006)
Physics
Condensed Matter
Statistical Mechanics
4 pages, 1 figure
Scientific paper
10.1103/PhysRevLett.97.100602
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 $\epsilon_{c}^{finite}$, jumping discontinuously to a different value $\epsilon_{c}^{infinite}$ in the thermodynamic limit. Remarkably, $\epsilon_{c}^{finite}$ 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.
Casetti Lapo
Kastner Michael
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