Universality and the five-dimensional Ising model

Abstract

We solve the long-standing discrepancy between Monte Carlo results and the renormalization prediction for the Binder cumulant of the five-dimensional Ising model. Our conclusions are based on accurate Monte Carlo data for systems with linear sizes up to L=22. A detailed analysis of the corrections to scaling allows the extrapolation of these results to L=\infinity. Our determination of the critical point, K_c=0.1139150 (4), is more than an order of magnitude more accurate than previous estimates.

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References in corpus (2)

• Finite-size Scaling and Universality above the Upper Critical Dimensionality
• Scaling above the upper critical dimension in Ising Models

Cited by in corpus (27)

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• Finite size scaling of the correlation length above the upper critical dimension
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• Fisher's scaling relation above the upper critical dimension
• The discontinuity of the specific heat for the 5D Ising model
• Scaling at quantum phase transitions above the upper critical dimension
• Monte Carlo investigations of phase transitions: status and perspectives
• Theoretical investigation of finite size effects at DNA melting
• Finite-size scaling of directed percolation above the upper critical dimension
• Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions
• Universality and nonmonotonic finite-size effects above the upper critical dimension
• Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings
• Finite-size scaling of directed percolation in the steady state
• Binder cumulants of an urn model and Ising model above critical dimension
• Ising spin glass models versus Ising models: an effective mapping at high temperature I. General result
• Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Complete graph asymptotics for the Ising and random cluster models on 5D grids with cyclic boundary
• Boundary effects on finite-size scaling for the 5-dimensional Ising model
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Monte Carlo Renormalization Group Analysis of Lattice ${\varphi }^4$ Model in $D=3,4$
• Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation
• Multirange Ising model on the square lattice
• On a previously unpublished work with Ralph Kenna