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

Abstract

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s >= 1/2 and for the lattice scalar field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices in four, five and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions, yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.

17 pages, 10 figures

References in corpus (12)

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Cited by in corpus (9)

• Hyperscaling above the upper critical dimension
• The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3
• Finite size scaling of the 5D Ising model with free boundary conditions
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 <= d <= 7
• Higher order expansions for the entropy of a dimer or a monomer-dimer system on d-dimensional lattices
• Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant
• On a previously unpublished work with Ralph Kenna