The Denaturation Transition Poland-Scheraga Models

The non-crossing constraint therefore becomes a hard wall constraint for the walk S and we are effectively dealing with the wetting model of Section 1.3 (with a particular choice of F(-)). In absence of constraint, the model falls of course in the class of models discussed in Section 1.2 and, as we have seen, the general models introduced in Section 1.2 include also the wetting models. In particular we have seen that the hard wall constraint induces simply a shift of the critical point. 

One can generalize the simple random walk model by considering for example a more realistic (1 - - 2)-dimensional model note that the noncrossing constraint looses meaning in this case, but in any case the difference of two random walks is still a random walk and the model reduces to pinning on a defect line. 

Before going into this issue, which is at the heart of much of the work 

The Poland Scheraga model is introduced by assigning the so called loop entropy S ) which is taken with the property 

Quite a bit of insight is gained once we observe that 

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