Universal amplitude ratios for scaling corrections on Ising strips with fixed boundary conditions

TL;DR

This paper investigates finite-size scaling corrections in the 2D Ising model on a strip with fixed boundary conditions, revealing universal amplitude ratios that are invariant under anisotropy changes and are explained by conformal perturbation theory.

Contribution

It identifies universal amplitude ratios for finite-size corrections in the Ising model with fixed boundaries and confirms their invariance under anisotropy variations using conformal perturbation theory.

Findings

Amplitude ratios $b_k^{(n)}/a_k$ are universal and invariant under anisotropy.

Finite-size corrections follow a specific power-law form $a_k/N^{2k-1}$.

Conformal perturbation theory accurately reproduces the universal ratios.

Abstract

We study the (analytic) finite-size corrections in the Ising model on the strip with fixed ($+ -$) boundary conditions. We find that subdominant finite-size corrections to scaling should be to the form $a_k/N^{2k-1}$ for the free energy $f_N$ and $b_k^{(n)}/N^{2k-1}$ for inverse correlation length $\xi_n^{-1}$, with integer value of $k$. We investigate the set $\{a_k, b_k^{(n)}\}$ by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios $b_k^{(n)}/a_k$ remain constant upon varying coupling anisotropy. Such universal behavior are correctly reproduced by the conformal perturbative approach.