Grad \(\phi\) perturbations of massless Gaussian fields (Q918051)

This paper (made of two parts, a survey plus the detailed technicalities) shows that the pressure of a continuum dipole gas is analytic. The partition function is written as a functional integral, using the sine- Gordon transformation; this functional integral is evaluated by a sequence of integrals associated with increasing length scales, and two well-adapted and natural objects playing the role of exponential and logarithm are introduced. The dipole gas is taken as an example to show a possible way to improve the work of \textit{K. Gawedzki} and \textit{A. Kupiainen} [Ann. Phys. 147, pp. 198 (1983); and Commun. Math. Phys. 92, pp. 531 (1984)].