Abstract
An Ising chain with Hamiltonian H=-J Sigma i<j epsilon ijSiSj/ mod i-j mod (1+ sigma )/2 is considered where the epsilon ij are independent random variables. According to Kotliar et al. (1983) this model has a phrase transition with non-mean-field exponents when 1/3< sigma <1 and mean-field exponents beyond the upper critical value of sigma =1/3. By means of an epsilon expansion about the lower critical value of sigma =1, the model is shown to be replica symmetric as epsilon to 0 and it is speculated that this result holds for 1/3< sigma <1.
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