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:1402.1657 · Nuclear Physics B

Hyperscaling above the upper critical dimension

Bertrand Berche, Ralph Kenna B, Jean‐Charles Walter

Published Jul 27, 2012• 71 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2012.07.021

Related papers

Hyperscaling and universality in 3 dimensions

Bernie G. Nickel

Physica A Statistical Mechanics and its Applications•Mar 1, 1981•56 citations

Hyperscaling and the critical exponentv

M.J. Holwerda, W.L.G.A.M. van Neerven, R. P. Van Royen

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields•Jul 1, 1979•2 citations

Hyperscaling Violation in Ising Spin Glasses

Ian A. Campbell, P. H. Lundow

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.

arXiv:1805.05478•Entropy•Oct 8, 2019•3 citations

Violations of Hyperscaling in Finite-Size Scaling above the Upper Critical Dimension

A. P. Young

We consider how finite-size scaling (FSS) is modified above the upper critical dimension, du=4, due to hyperscaling violations, which in turn arise from a dangerous irrelevant variable. In addition to the commonly studied case of periodic boundary conditions, we also consider new effects that arise with free boundary conditions. Some numerical results are presented in addition to theoretical arguments.

Entropy•Jun 12, 2024•3 citations

Near lower critical dimension

Igor F. Herbut

Cambridge University Press eBooks•Jan 4, 2007•0 citations

A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa'

Kenna, Bertrand Berche

It is well known that standard hyperscaling breaks down above the upper critical dimension d c , where the critical exponents take on their Landau values.Here, we show that this is because in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale.However, the correlationlength scale and the underlying length scale of the system are not the same at or above the upper critical dimension.Above d c they are related algebraically through a new critical exponent , while at d c they differ through logarithmic corrections governed by an exponent .Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions.

arXiv:1411.2754•Condensed Matter Physics•Jan 1, 2013•44 citations
In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.
It is well known that standard hyperscaling breaks down above the upper critical dimension d c , where the critical exponents take on their Landau values.Here, we show that this is because in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale.However, the correlationlength scale and the underlying length scale of the system are not the same at or above the upper critical dimension.Above d c they are related algebraically through a new critical exponent , while at d c they differ through logarithmic corrections governed by an exponent .Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions.