Infinite lattice models by an expansion with a non-Gaussian initial approximation

Abstract

Recently, a convergent series employing a non-Gaussian initial approximation was constructed and shown to be an effective computational tool for the finite size lattice models with a polynomial interaction. Here we show that the Borel summability is a sufficient condition for the correctness of the convergent series applied to infinite lattice models. We test the numerical workability of the convergent series method by examine one-and two-dimensional φ 4 -infinite lattice models. The comparison of the convergent series computations and the infinite lattice extrapolations of the Monte Carlo simulations reveals an agreement between two approaches.