Critical scaling for spectral functions

TL;DR

This paper investigates the critical behavior of spectral functions in 2+1 dimensional scalar ^4 theory near phase transition, using spectral functional methods to extract scaling exponents and compare with Euclidean analyses.

Contribution

It introduces a spectral functional Callan-Symanzik approach that maintains Lorentz invariance and causality for studying critical spectral functions.

Findings

Extracted the critical exponent  from spectral functions.

Compared spectral and Euclidean fixed point results.

Validated the spectral functional approach for critical phenomena.

Abstract

We study real-time scalar $\phi^4$-theory in 2+1 dimensions near criticality. Specifically, we compute the single-particle spectral function and that of the $s$-channel four-point function in and outside the scaling regime. The computation is done with the spectral functional Callan-Symanzik equation, which exhibits manifest Lorentz invariance and preserves causality. We extract the scaling exponent $\eta$ from the spectral function and compare our result with that from a Euclidean fixed point analysis.