Interaction effects in the spectrum of the three-dimensional Ising model

TL;DR

This paper investigates how interaction effects influence the long-distance behavior of correlation functions in the 3D Ising model, emphasizing the importance of accounting for these effects in data analysis.

Contribution

It provides a one-loop calculation demonstrating the significance of interaction effects on correlation functions in the 3D Ising model's broken-symmetry phase.

Findings

Interaction effects are non-negligible up to a few correlation lengths.

Interaction effects influence the interpretation of Monte Carlo data.

Long-distance correlations are affected by virtual pair creation and annihilation.

Abstract

The two-point correlation functions of statistical models show in general both poles and cuts in momentum space. The former correspond to the spectrum of massive excitations of the model, while the latter originate from interaction effects, namely creation and annihilation of virtual pairs of excitations. We discuss the effect of such interactions on the long distance behavior of correlation functions in configuration space, focusing on certain time-slice operators which are commonly used to extract the spectrum. For the 3D Ising model in the scaling region of the broken-symmetry phase, a one-loop calculation shows that the interaction effects on time-slice correlations is non negligible for distances up to a few times the correlation length, and should therefore be taken into account when analysing Monte Carlo data.