Longitudinal and transverse spectral functions in the three-dimensional O(4) model

TL;DR

This study uses high-statistics simulations and maximum entropy analysis to explore the spectral functions of the 3D O(4) model, revealing sharp peaks and continuum states across different temperature regimes, and confirming theoretical relations.

Contribution

It provides detailed spectral function analysis of the 3D O(4) model near criticality using maximum entropy, and confirms the Patashinskii-Pokrovskii relation.

Findings

Transverse spectral function shows a sharp peak at all T and H.

Longitudinal spectral function exhibits a peak at T>T_c that broadens near T_c.

Below T_c, a continuum of states appears at higher energies.

Abstract

We have performed a high statistics simulation of the O(4) model on a three-dimensional lattice of linear extension L=120 for small external fields H. Using the maximum entropy method we analyze the longitudinal and transverse plane spin correlation functions for T<T_c and T>=T_c. In the transverse case we find for all T and H a single sharp peak in the spectral function, whose position defines the transverse mass m_T, the correlator is that of a free particle with mass m_T. In the longitudinal case we find in the very high temperature region also a single sharp peak in the spectrum. On approaching the critical point from above the peak broadens somewhat and at T_c its position m_L is at 2m_T for all our H-values. Below T_c we find still a significant peak at omega=2m_T and at higher omega-values a continuum of states with several smaller peaks with decreasing heights. This finding is in accord with a relation of Patashinskii and Pokrovskii between the longitudinal and the transverse correlation functions. We test this relation in the following. As a by-product we calculate critical exponents and amplitudes and confirm our former results.