Conformal field theory of the Flory model of polymer melting

TL;DR

This paper develops a conformal field theory framework for the Flory model of polymer melting, providing exact critical parameters and demonstrating the continuous nature of the phase transition, contrasting mean-field predictions.

Contribution

It introduces a conformal field theory description of the Flory polymer melting model, linking it to known solvable models and calculating exact critical exponents.

Findings

Polymer melting is a continuous phase transition.

Exact critical exponents are computed for the model.

The theory aligns with numerical transfer matrix results.

Abstract

We study the scaling limit of a fully packed loop model in two dimensions, where the loops are endowed with a bending rigidity. The scaling limit is described by a three-parameter family of conformal field theories, which we characterize via its Coulomb-gas representation. One choice for two of the three parameters reproduces the critical line of the exactly solvable six-vertex model, while another corresponds to the Flory model of polymer melting. Exact central charge and critical exponents are calculated for polymer melting in two dimensions. Contrary to predictions from mean-field theory we show that polymer melting, as described by the Flory model, is continuous. We test our field theoretical results against numerical transfer matrix calculations.