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

Engels J, Vogt O (2010)

NUCLEAR PHYSICS B 832(3): 538-566.

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Engels, Jürgen

^{UniBi}; Vogt, O.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 and its range of applicability in the following. As a by-product we calculate critical exponents and amplitudes and confirm our former results. (C) 2010 Elsevier B.V. All rights reserved.

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### Cite this

Engels J, Vogt O. Longitudinal and transverse spectral functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*. 2010;832(3):538-566.Engels, J., & Vogt, O. (2010). Longitudinal and transverse spectral functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*,*832*(3), 538-566. doi:10.1016/j.nuclphysb.2010.02.006Engels, J., and Vogt, O. (2010). Longitudinal and transverse spectral functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*832, 538-566.Engels, J., & Vogt, O., 2010. Longitudinal and transverse spectral functions in the three-dimensional O(4) model.

*NUCLEAR PHYSICS B*, 832(3), p 538-566. J. Engels and O. Vogt, “Longitudinal and transverse spectral functions in the three-dimensional O(4) model”,

*NUCLEAR PHYSICS B*, vol. 832, 2010, pp. 538-566. Engels, J., Vogt, O.: Longitudinal and transverse spectral functions in the three-dimensional O(4) model. NUCLEAR PHYSICS B. 832, 538-566 (2010).

Engels, Jürgen, and Vogt, O. “Longitudinal and transverse spectral functions in the three-dimensional O(4) model”.

*NUCLEAR PHYSICS B*832.3 (2010): 538-566.
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