Causality and dissipation in relativistic polarizeable fluids

TL;DR

This paper investigates how causality breaks down in relativistic polarizable fluids and proposes a modified framework with dissipation to restore causality, highlighting implications for ferromagnetic materials and spontaneous magnetization.

Contribution

It introduces a relaxation term linking vorticity and polarization to restore causality in relativistic polarizable fluids, providing a new causal Lagrangian near the perfect fluid limit.

Findings

A relaxation term is necessary to restore causality.

A minimum dissipation level is required for causality.

Infrared acausal modes indicate spontaneous magnetization in ferromagnetic materials.

Abstract

We analyze the breakdown of causality for the perfect fluid limit in a medium with polarizeability. We show that to restore causality a relaxation term linking vorticity and polarization, analogous to the Israel-Stewart term linking viscous forces and gradients,is required. This term provides a minimum amount of dissipation a locally thermalized relativistic medium with polarizeability must have, independently of its underlying degrees of freedom. For ferromagnetic materials an infrared acausal mode remains, which we interpret as a Banks-Casher mode signaling spontaneous magnetization. With these ingredients, we propose a candidate for a fully causal Lagrangian of a relativistic polarizeable system near the perfect fluid limit.