# Universality of Pattern Formation

## TL;DR

This paper investigates pattern formation in a $ ext{PT}$-symmetric scalar field theory, revealing a connection to tachyonic instabilities and proposing new universality classes, with implications for QCD phase behavior.

## Contribution

It introduces a novel analysis of pattern formation in $ ext{PT}$-symmetric field theories and extends this to multicomponent models, identifying new universality classes and potential QCD applications.

## Key findings

- Pattern formation linked to tachyonic instabilities.
- Pattern morphologies vary smoothly without microphases.
- Potential patterns of confined and deconfined matter in QCD.

## Abstract

We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region. Analytical results and simulations associate pattern formation with tachyonic instabilities in the homogeneous phase. Monte Carlo simulation shows that pattern morphologies vary smoothly, without distinct microphases. We suggest that pattern formation in this model may be regarded as a form of arrested spinodal decomposition. We extend our theoretical analysis to multicomponent $\mathcal PT$-symmetric Euclidean scalar field theories and show that they give rise to new universality classes of local field theories that exhibit patterned behavior in the critical region. QCD at finite temperature and density is a member of the $Z(2)$ universality class when the Polyakov loop is used to distinguish confined and deconfined phases. This suggests the possibility of the formation of patterns of confined and deconfined matter in QCD in the critical region in the $\mu-T$ plane.