The 2n-point renormalized coupling constants in the 3d Ising model: estimates by high temperature series to order beta^17

Abstract

We compute the 2n-point renormalized coupling constants in the symmetric phase of the 3d Ising model on the sc lattice in terms of the high temperature expansions O(beta^{17}) of the Fourier transformed 2n-point connected correlation functions at zero momentum. Our high temperature estimates of these quantities, which enter into the small field expansion of the effective potential for a 3d scalar field at the IR fixed point or, equivalently, in the critical equation of state of the 3d Ising model universality class, are compared with recent results obtained by renormalization group methods, strong coupling, stochastic simulations as well as previous high temperature expansions.