The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$

TL;DR

This paper uses the form factor bootstrap method to exactly compute the large-distance behavior of the spin-spin correlation function in the 2D Ising model at critical temperature with a magnetic field, revealing complex analytic structures.

Contribution

It provides the first exact spectral series expansion for the correlation function in this setting, demonstrating rapid convergence and agreement with numerical results.

Findings

Spectral series converges rapidly.

Exact correlation function matches numerical data.

Analytic structure influenced by multi-particle scattering.

Abstract

The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $<\sigma(x) \sigma(0)>$ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $\sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.