Finite-size corrections for logarithmic representations in critical dense polymers

TL;DR

This paper investigates finite-size corrections in the dense polymer model at criticality, revealing that while corrections are non-universal, their ratios are universal and unaffected by Jordan cells or indecomposable representation parameters.

Contribution

The study extends conformal perturbation theory to include Jordan cells and analyzes their impact on finite-size corrections in dense polymers.

Findings

Finite-size corrections are independent of Jordan cells at first order.

Ratios of finite-size corrections are universal.

Conformal perturbation theory accurately predicts correction ratios.

Abstract

We study (analytic) finite-size corrections in the dense polymer model on the strip by perturbing the critical Hamiltonian with irrelevant operators belonging to the tower of the identity. We generalize the perturbation expansion to include Jordan cells, and examine whether the finite-size corrections are sensitive to the properties of indecomposable representations appearing in the conformal spectrum, in particular their indecomposability parameters. We find, at first order, that the corrections do not depend on these parameters nor even on the presence of Jordan cells. Though the corrections themselves are not universal, the ratios are universal and correctly reproduced by the conformal perturbative approach, to first order.