van Enter, Aernout

van Hemmen, JL

An Ising chain is considered with a potential of the form J(i,j)/|i-j|^α where the J(i,j) are independent random variables with mean zero. The chain contains both randomness and frustration, and serves to model a spin glass. A simple argument is provided to show that the system does not exhibit a phase transition at a positive temperature if α&gt;1. This is to be contrasted with a ferromagnetic interaction which requires α&gt;2. The basic idea is to prove that the "surface" free energy between two half-lines is finite, although the "surface" energy may be unbounded. For d-dimensional systems, it is shown that the free energy does not depend on the specific boundary conditions if α&gt;(1/2)d

Absence of Phase Transitions in Certain One-Dimensional Long-Range Random Systems

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Proceedings - University of Groningen