Extended Scaling in High Dimensions

Abstract

We apply and test the recently proposed "extended scaling" scheme in an analysis of the magnetic susceptibility of Ising systems above the upper critical dimension. The data are obtained by Monte Carlo simulations using both the conventional Wolff cluster algorithm and the Prokof'ev-Svistunov worm algorithm. As already observed for other models, extended scaling is shown to extend the high-temperature critical scaling regime over a range of temperatures much wider than that achieved conventionally. It allows for an accurate determination of leading and sub-leading scaling indices, critical temperatures and amplitudes of the confluent corrections.

16 pages, 8 figures. Improved version to appear in JSTAT

References in corpus (8)

• Worm algorithms for classical statistical models
• Renormalization Group Analysis of Finite-Size Scaling in the ${\Phi }_4^4$ Model
• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses
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Cited by in corpus (15)

• An introduction to Monte Carlo methods
• Hyperscaling above the upper critical dimension
• Finite size scaling of the 5D Ising model with free boundary conditions
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• The discontinuity of the specific heat for the 5D Ising model
• The worm process for the Ising model is rapidly mixing
• An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice
• The bimodal and Gaussian Ising Spin Glasses in dimension two revisited
• 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
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions
• The Ising universality class in dimension three: corrections to scaling
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension
• Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant
• On a previously unpublished work with Ralph Kenna
• The Ising ferromagnet in dimension five: link and spin overlaps