Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 40: Critical Phenomena and Phase Transitions I

DY 40.3: Vortrag

Donnerstag, 30. März 2006, 10:15–10:30, H\"UL 186

Finite-size behaviour of the microcanonical specific heat — •Hans Behringer¹ and Michel Pleimling² — ¹Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld — ²Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, D-91058 Erlangen

The basic quantity in the microcanonical approach to statistical properties of physical systems is the entropy S(E) = lnΩ(E) where Ω(E) is the density of states as a function of the energy. The specific heat of the system is related to the inverse of the curvature of the entropy. The behaviour of the microcanonical specific heat of systems that undergo a continuous phase transition in the thermodynamic limit is investigated for finite systems. The numerical study of small Ising and Potts systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size in contrast to a canonical treatment where the maximum of the specific heat increases monotonically with the system size. A general phenomenological theory is developed which permits a description of this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of the microcanonical critical exponents from asymptotically large systems. In the case of the Baxter-Wu model the microcanonical analysis reveals a behaviour of the specific heat that suggests at first sight the appearance of a discontinuous phase transition in the infinite volume limit contrary to the known continuous character. However, the proposed phenomenological theory shows that this peculiar behaviour stems from a finite-size effect which disappears in the thermodynamic limit and therefore the observations are consistent with the continuous phase transition of in the Baxter-Wu model.