2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/28291A new duality relation is derived for the Potts model in one dimension. It is shown that the partition function is self-dual with the nearest-neighbor interaction and the external field appearing as dual parameters. Zeroes of the partition function are analyzed. Particularly, we show that the new duality relation implies a circle theorem in the complex temperature plane for the one-dimensional Ising model.RevTex file, 6 pages, 1 fig, submitted to Physics Letters AStatistical Mechanicstext