NON-EXISTENCE OF SPONTANEOUS MAGNETIZATION IN A ONE-DIMENSIONAL ISING FERROMAGNET

It is proved that an infinite linear chain of spins μj=±1, with an interaction energy {Mathematical expression} has zero spontaneous magnetization at all finite temperatures, provided that J (n) is non-negative and that {Mathematical expression}. This shows that a theorem of Ruelle, establishing the absence of long-range order when the sum Σn J (n) converges, is not the best possible. © 1969 Springer-Verlag.