Exactly solvable model with an unusual phase transition: the rolling transition of a pinned Gaussian chain

We consider a Gaussian polymer chain in an external potential field of a He aviside form. The chain is constrained by one of its ends to the point wher e the potential changes. For this model, the exact partition function is av ailable. In the appropriate thermodynamic limit the chain 'rolls' from one half-space to the other upon changing the sign of the external potential by way of a rather special phase transition. The derivative of the free energ y is discontinuous indicating a first-order character. Its complex zero dis tribution is consistent with literature predictions for this. However, from the exact analytical equation for the Landau function it is found that the re are no metastable states associated with the transition. Moreover, the d erivative of the energy is discontinuous pointing to a second order classif ication. Finally, there are no singularities with respect of derivatives of the entropy. All this is consistent with the hypothesis that the model fea tures a (multi) critical point at the condition that the potential changes sign. (C) 2001 Elsevier Science B.V. All rights reserved.