Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9904297

On a trivial aspect of canonical specific heat scaling

M. Promberger

Published Apr 21, 1999• 4 citations
arXivHTMLPDF

Abstract

We show that the canonical finite size scaling of the specific heat emerges naturally - and in some sense trivially - from the assumption that the microcanonical specific entropy exhibits no substantial system size dependence.
DOI
10.48550/arxiv.cond-mat/9904297

Related papers

Finite-size behaviour of the microcanonical specific heat

H Behringer, M Pleimling, A Hüller

For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.

arXiv:cond-mat/0411153•Journal of Physics A Mathematical and General•Jan 20, 2005•24 citations

Critical-point finite-size scaling in the microcanonical ensemble

Ann Bruce, Nigel B. Wilding

We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.

arXiv:cond-mat/9908025•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Oct 1, 1999•14 citations

Consistency of Microcanonical and Canonical Finite-Size Scaling

Michael Kästner, M. Promberger

arXiv:cond-mat/0008106•Journal of Statistical Physics•Jun 1, 2001•6 citations

Qualitative Picture of Scaling in the Entropy Formalism

Hans Behringer

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.

Entropy•Sep 5, 2008•4 citations

Finite-size Scaling Considerations on the Ground State Microcanonical Temperature in Entropic Sampling Simulations

Álvaro A. Caparica, Cláudio José DaSilva

arXiv:1112.1907•Brazilian Journal of Physics•Sep 8, 2015•6 citations

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

L. A. Fernández, A. Gordillo-Guerrero, Víctor Martín-Mayor +1 more

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization (the so-called quotients method) to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, eta, and of the (Fisher-renormalized) thermal nu exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

arXiv:0905.4029•Physical Review E•Nov 6, 2009•8 citations
For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits us to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.
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.
A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization (the so-called quotients method) to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, eta, and of the (Fisher-renormalized) thermal nu exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.