Symmetries of microcanonical entropy surfaces

Pleimling

2006

Phys. Rev. E

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The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as, for example, in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.

Section: Signatures Of Phase Transitions In the Microcanonical Spmentioning

confidence: 91%

Continuous phase transitions with a convex dip in the microcanonical entropy

Pleimling

2006

Phys. Rev. E

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“…The asymptotic expression (35) is chosen to reproduce the singular asymptotic behaviour of physical quantities which is deduced from the scaling relation (15). Note, however, that certain properties of the internal energy -for an entropy below the critical point, for instance, it has to be constant for magnetisations in the interval [−m sp , m sp ] -are not yet incorporated in (35), but the argumentation to follow still applies to the concave envelop function of (35) with respect to the magnetisation direction.…”

Section: General Entropymentioning

confidence: 99%

“…The description of phase transitions in the entropy or microcanonical formalism has gained growing interest in recent years [5][6][7][8][9][10][11][12][13][14][15][16]18]. Apart from the study of discontinuous transitions in spin systems some works also investigated continuous phase transitions in the microcanonical approach [11,14,16,17,19,20].…”

Section: Introductionmentioning

confidence: 99%

Qualitative Picture of Scaling in the Entropy Formalism

2008

Entropy

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The properties of an infinite system at a continuous phase transition are characterised by non-trivial critical exponents. These non-trivial exponents are related to scaling relations of the thermodynamic potential. The scaling properties of the singular part of the specific entropy of infinite systems are deduced starting from the well-established scaling relations of the Gibbs free energy. Moreover, it turns out that the corrections to scaling are suppressed in the microcanonical ensemble compared to the corresponding corrections in the canonical ensemble

“…In any finite system one does not observe diverging quantities but only rounded maxima. This is, however, completely different in the microcanonical ensemble where the features of spontaneous symmetry breaking turn up already for finite systems [10,12,17,13,15,16,21]. It is instructive to first inspect directly the entropy surface s(e, m).…”

Section: Signatures In Small Systemsmentioning

confidence: 99%

Microcanonical analysis of small systems

Pleimling

2005

Phase Transitions

The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from the entropy. Response functions such as the susceptibility are for example related to the curvature of the entropy surface. Interestingly, physical quantities in the microcanonical ensemble show characteristic properties of phase transitions already in finite systems. In this paper we investigate these characteristics for finite Ising systems. The singularities in microcanonical quantities which announce a continuous phase transition in the infinite system are characterised by classical critical exponents. Estimates of the non-classical exponents which emerge only in the thermodynamic limit can nevertheless be obtained by analyzing effective exponents or by applying a microcanonical finite-size scaling theory. This is explicitly demonstrated for two-and three-dimensional Ising systems.