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The interface roughening phenomenon is formulated in terms of a statistical model of thermally created atomic steps. The simple case of a length-proportional energy is equivalent to known roughening models featuring an infinite-order roughening phase transition with an exponentially diverging correlation length and interface thickness. If, in addition, a step bending energy is included which is different for up- and down-steps, the sharp roughening transition is destroyed and the correlation length and the interface thickness remain finite Hence, in this case, a roughening or surface melting transition is absent. Some estimates on the observability of this result, which has consequence, e.g. for the structural behaviour of solid surfaces and on the crystal growth mechanism, are made.

A recently proposed statistical model for the two-dimensional reconstruction transition of H/Ni(110) is investigated using a suitable fast Monte Carlo formalism. The phase diagram is presented for some range of the parameter values. Various low temperature (LT) non-reconstructed, and homogeneous and pairing-row reconstructed phases are found. Near the phase boundaries the approach to equilibrium is strongly slowed down due to topological constraints. Similar features are reported from experimental studies on the clean Pd(110) surface.