In this article we address a well known problem at the intersection of ergodic theory and statistical mechanics. We prove that there exists a continuous eigenfunction for the transfer operator corresponding to pair potentials that satisfy a square summability condition on the variations, when the inverse temperature is subcritical. As a corollary we obtain a continuous eigenfunction for the classical Dyson model, with interactions J(k)=βk−α, k≥1, in the whole subcritical regime β<βc for which the parameter α is greater than 3/2.