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High-temperature expansions are presently the only viable approach to thenumerical calculation of the higher susceptibilities for the spin and thescalar-field models on high-dimensional lattices. The critical amplitudes ofthese quantities enter into a sequence of universal amplitude-ratios whichdetermine the critical equation of state. We have obtained a substantialextension through order 24, of the high-temperature expansions of the freeenergy (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, onthe simple-cubic and the body-centered-cubic lattices in four, five and sixspatial dimensions. A numerical analysis of the higher susceptibilitiesobtained from these expansions, yields results consistent with the widelyaccepted ideas, based on the renormalization group and the constructiveapproach to Euclidean quantum field theory, concerning the no-interaction("triviality") property of the continuum (scaling) limit of spin-s Ising andlattice scalar-field models at and above the upper critical dimensionality.

physical review. e, statistical, nonlinear and soft matter physics

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