Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field

TL;DR

This paper calculates the mass spectrum and critical amplitudes of the 2D Ising model in a magnetic field using transfer matrix methods, confirming theoretical predictions and providing new amplitude data.

Contribution

It provides the first precise transfer matrix computations of the 2D Ising model's spectrum in a magnetic field, aligning with S-matrix and conformal field theory predictions.

Findings

Mass spectrum matches theoretical predictions

Critical amplitudes are accurately computed

Subleading correction amplitudes are obtained

Abstract

We compute the spectrum and several critical amplitudes of the two dimensional Ising model in a magnetic field with the transfer matrix method. The three lightest masses and their overlaps with the spin and the energy operators are computed on lattices of a width up to L=21. In extracting the continuum results we also take into account the corrections to scaling due to irrelevant operators. In contrast with previous Monte Carlo simulations our final results are in perfect agreement with the predictions of S-matrix and conformal field theory. We also obtain the amplitudes of some of the subleading corrections, for which no S-matrix prediction has yet been obtained.