Finite-temperature correlation function for the one-dimensional quantum Ising model: The virial expansion

We rewrite the exact expression for the finite-temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial expansion (expansion in powers of the soliton density).

Figure 1

A graphic representation of Eq. (9). The ellipses are form factors of the $\sigma$ operator. Lines with left arrows are $f^{(+)}\left(\theta \right)\exp \left[itϵ\right(\theta )+ixp(\theta )$, lines with right arrows are $f^{(-)}\left(\theta \right)\exp [-itϵ(\theta )-ixp(\theta \left)\right]$.