Improved harmonic approximation and the 2D Ising model at $T\neq T_{c}$ and $h\neq0$

Abstract

We propose a new method to determine the unknown parameter associated to a self-consistent harmonic approximation. We check the validity of our technique in the context of the sine-Gordon model. As a non trivial application we consider the scaling regime of the 2D Ising model away from the critical point and in the presence of a magnetic field $h$. We derive an expression that relates the approximate correlation length $\xi$, $T-T_c$ and $h$.