Finite-size behaviour of the microcanonical specific heat

Behrinǵer, Hans; Pleimling, Michel; Hueller, Alfred

doi:10.1088/0305-4470/38/5/001

Cited by 21 publications

(35 citation statements)

References 32 publications

(65 reference statements)

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“…Whereas in (a) we consider a system with periodic boundary conditions composed of N = 8 × 8 × 8 spins, with J xy = J z , in (b) and (c) we show two systems of N = 8 × 8 × 8 sites with free boundary condition in z direction, the different systems having different relative strengths of the interactions: In a microcanonical analysis one infers the physical property of a system from a direct study of the microcanonical entropy S(e, m). 36,37 Most investigations of this type focused on spin models with ferromagnetic nearest neighbor interactions, as for example the standard Ising or Potts models, [38][39][40][41][42][43][44][45][46] or on polymer models. 47,48 Due to its complicated interactions, the microcanonical entropy of the Ising metamagnet is more complex as, for example, that of the standard nearest neighbor Ising model, 37 see Fig.…”

Section: A the Density Of Statesmentioning

confidence: 99%

Ising metamagnets in thin film geometry: Equilibrium properties

Chou

Pleimling

2011

Phys. Rev. B

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Artificial antiferromagnets and synthetic metamagnets have attracted much attention recently due to their potential for many different applications. Under some simplifying assumptions these systems can be modeled by thin Ising metamagnetic films. In this paper we study, using both the Wang/Landau scheme and importance sampling Monte Carlo simulations, the equilibrium properties of these films. On the one hand we discuss the microcanonical density of states and its prominent features. On the other we analyze canonically various global and layer quantities. We obtain the phase diagram of thin Ising metamagnets as a function of temperature and external magnetic field. Whereas the phase diagram of the bulk system only exhibits one phase transition between the antiferromagnetic and paramagnetic phases, the phase diagram of thin Ising metamagnets includes an additional intermediate phase where one of the surface layers has aligned itself with the direction of the applied magnetic field. This additional phase transition is discontinuous and ends in a critical end point. Consequently, it is possible to gradually go from the antiferromagnetic phase to the intermediate phase without passing through a phase transition.

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Section: A the Density Of Statesmentioning

confidence: 99%

Ising metamagnets in thin film geometry: Equilibrium properties

Chou

Pleimling

2011

Phys. Rev. B

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“…This makes it difficult to identify the phase transition and to determine its order 27 . By contrast, if such finite systems are studied using the microcanonical ensemble, the phase transitions are directly detected [28][29][30][31] . Unfortunately, however, the microcanonical ensemble has technical difficulties in practical calculations.…”

Section: Introductionmentioning

confidence: 99%

Squeezed ensemble for systems with first-order phase transitions

Yoneta

Shimizu

2019

Phys. Rev. B

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All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition region, one must choose an appropriate statistical ensemble. The appropriate choice is particularly important when one investigates finite systems, for which even the equivalence of ensembles does not hold. We propose a class of statistical ensembles, which always give the correct equilibrium state even in the first-order phase transition region. We derive various formulas for this class of ensembles, including the one by which temperature is obtained directly from energy without knowing entropy. Moreover, these ensembles are convenient for practical calculations because of good analytic properties. We also derive formulas which relate statistical-mechanical quantities of different ensembles, including the conventional ones, for finite systems. The formulas are useful for obtaining results with smaller finite size effects, and for improving the computational efficiency. The advantages of the squeezed ensembles are confirmed by applying them to the Heisenberg model and the frustrated Ising model. arXiv:1903.04111v2 [cond-mat.stat-mech]

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“…In the case of biological macromolecules such a proteins, which are heteropolymers of fixed length, no such thermodynamic limit exits, even hypothetically. However, in such cases one can still make use of a microcanonical analysis to define phase transitions in finite size systems [2,3].…”

Section: Introductionmentioning

confidence: 99%

Two-state protein-like folding of a homopolymer chain

2010

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Many small proteins fold via a first-order "all-or-none" transition directly from an expanded coil to a compact native state. Here we study an analogous direct freezing transition from an expanded coil to a compact crystallite for a simple flexible homopolymer. Wang-Landau sampling is used to construct the 1D density of states for square-well chains of length 128. Analysis within both the micro-canonical and canonical ensembles shows that, for a chain with sufficiently short-range interactions, the usual polymer collapse transition is preempted by a direct freezing or "folding" transition. A 2D free-energy landscape, built via subsequent multi-canonical sampling, reveals a dominant folding pathway over a single free-energy barrier. This barrier separates a high entropy ensemble of unfolded states from a low entropy set of crystallite states and the transition proceeds via the formation of a transition-state folding nucleus. Despite the non-unique homopolymer ground state, the thermodynamics of this direct freezing transition are identical to the thermodynamics of two-state protein folding. The model chain satisfies the van't Hoff calorimetric criterion for two-state folding and an Arrhenius analysis of the folding/unfolding free energy barrier yields a Chevron plot characteristic of small proteins.

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Finite-size behaviour of the microcanonical specific heat

Cited by 21 publications

References 32 publications

Ising metamagnets in thin film geometry: Equilibrium properties

Ising metamagnets in thin film geometry: Equilibrium properties

Squeezed ensemble for systems with first-order phase transitions

Two-state protein-like folding of a homopolymer chain

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