Roughening-induced deconstruction in (100) facets of CsCl-type crystals

The staggered six-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl-type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully packed loop-gas line. We prove that the reconstruction and roughening transitions, cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong-coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.