Diffusive-Ballistic Transition in Random Polymers with Drifts and Repulsive Long-Range Interactions

This paper leads with a random polymer model in $\Z^2$ having long-range self-repulsive interactions. By comparison with a long range one-dimensional ferromagnetic Ising model we shown that the polymer models we considered here undergo a phase transition in terms of the inverse temperature $β$. In the second part of this work we shown, using the Lee-Yang Circle Theorem, that our random polymer model with drifts satisfies the, Wu Liming [7], $C^2$ regularity condition. As consequence we obtain a Central Limit Theorem for the model.

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