Dynamic critical phenomena from spectral functions on the lattice

TL;DR

This paper uses real-time lattice simulations to study spectral functions near the critical temperature of a second-order phase transition, verifying the dynamic universality class of the relativistic scalar field theory.

Contribution

It computes spectral functions and the dynamic critical exponent z from first principles, confirming the universality class of the model.

Findings

Spectral functions follow universal scaling functions.

The dynamic critical exponent z is extracted.

The relativistic scalar field theory belongs to Model C universality class.

Abstract

We investigate spectral functions in the vicinity of the critical temperature of a second-order phase transition. Since critical phenomena in quantum field theories are governed by classical dynamics, universal properties can be computed using real-time lattice simulations. For the example of a relativistic single-component scalar field theory in 2+1 dimensions, we compute the spectral function described by universal scaling functions and extract the dynamic critical exponent z. Together with exactly known static properties of this theory, we obtain a verification from first principles that the relativistic theory is well described by the dynamic universality class of relaxational models with conserved density (Model C).