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This does not mean that the roughening transition is out of the scope of the cluster variation method or, more generally, of a mean-field theory. In fact, an analysis of the generalized susceptibility matrix may be used to localize a roughening transition. This approach consists in looking for the singularities of the matrix of the second derivative of the free energy functional (which is the inverse of the susceptibility matrix) for a 3D system that contains an interface with a step. For more details, see Refs. 42 and 43
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This does not mean that the roughening transition is out of the scope of the cluster variation method or, more generally, of a mean-field theory. In fact, an analysis of the generalized susceptibility matrix may be used to localize a roughening transition. This approach consists in looking for the singularities of the matrix of the second derivative of the free energy functional (which is the inverse of the susceptibility matrix) for a 3D system that contains an interface with a step. For more details, see Refs. 42 and 43.
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