We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interactions, since such a system is physically realized in the insulator $\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_4$. The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.

• Received 12 May 2005

DOI:https://doi.org/10.1103/PhysRevB.72.064411