Superroughening in the Ising chain with long-range interactions

We present a numerical study of the self-affine profiles obtained from configurations of the Ising model in d=1 with long-range interactions decaying with distance r as J(r) r−(1+ζ) for the cases ζ=0.3 and 0.5. The second-order static phase transition of this model is located by sharp changes in the values of the Hurst (H) and roughness (α) exponents, characterizing those profiles. The low-temperature phase corresponds to flat (α H 1) profiles, whereas the high-temperature phase is associated with rough (α H 0.5) ones. In the vicinity of the critical temperature we obtained superroughening, i.e., α>1≠H.