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

TL;DR

This paper investigates a random polymer model with long-range repulsive interactions and drifts, demonstrating a phase transition and establishing a Central Limit Theorem through advanced mathematical techniques.

Contribution

It introduces a novel analysis of a 2D random polymer with long-range interactions, showing phase transition behavior and proving regularity and CLT results.

Findings

Phase transition in inverse temperature β

Satisfaction of Wu Liming's C^2 regularity condition

Central Limit Theorem established for the model

Abstract

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 $\beta$. 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.