Bundles of Interacting Strings in Two Dimensions

TL;DR

This paper analytically studies two-dimensional bundles of interacting strings, revealing unbinding transitions and scaling behaviors, with results applicable to large N and interactions with boundaries.

Contribution

It provides an exact analytical solution for the transfer matrix of interacting string bundles of arbitrary size using Bethe ansatz methods.

Findings

Bundles exhibit a unique unbinding transition.

Interaction with a hard wall can cause one or multiple unbinding transitions.

Critical exponents are independent of bundle size N.

Abstract

Bundles of strings which interact via short-ranged pair potentials are studied in two dimensions. The corresponding transfer matrix problem is solved analytically for arbitrary string number N by Bethe ansatz methods. Bundles consisting of N identical strings exhibit a unique unbinding transition. If the string bundle interacts with a hard wall, the bundle may unbind from the wall via a unique transition or a sequence of N successive transitions. In all cases, the critical exponents are independent of N and the density profile of the strings exhibits a scaling form that approaches a mean-field profile in the limit of large N.