Abstract
We study an Ising model in one dimension with short range ferromagnetic and long range (power law) antiferromagnetic interactions. We show that the zero temperature phase diagram in a (longitudinal) field H involves a sequence of up and down domains whose size varies continuously with H, between -H_c and H_c which represent the edge of the ferromagnetic up and down phases. The implications of long range interaction in many body systems are discussed.
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