# Crystal structures in generalized Skyrme model

## TL;DR

This paper explores the properties and phase transitions of triply-periodic Skyrme crystals within a generalized model including higher-derivative terms, analyzing various potentials and submodels to understand their phase behavior.

## Contribution

It introduces a comprehensive study of Skyrme crystals with higher-derivative terms and different potentials, revealing phase transitions and the existence of crystals in simplified submodels.

## Key findings

- Skyrme crystals can exist in pure $ ext{L}_4$ and $ ext{L}_6$ models.
- Phase transitions from low-density quasi-liquid to high-density symmetric phases are observed.
- Different potential terms influence the phase structure and properties of the crystals.

## Abstract

We investigate the properties of triply-periodic Skyrme crystals in the generalized Skyrme model $\mathcal{L}_6 + \mathcal{L}_4 + \mathcal{L}_2+ \mathcal{L}_0$ with higher-derivative terms up to sixth order. Three different symmetry breaking potential terms $\mathcal{L}_0$ are considered, the generalized pion mass term, double vacuum potential and mixed potential. Various scenario of phase transitions from the low density phase to the high density phase are examined for different choices of the parameters of the model. In particular, we investigated limiting behavior of the Skyrme crystals in the truncated submodel without the Skyrme term $\mathcal{L}_4$ and/or without the $\mathcal{L}_2$ term. We show that the Skyrme crystal may exist in the pure $\mathcal{L}_4$ and $\mathcal{L}_6$ models and investigated the phase structure of these solutions. Considering the near-BPS submodel, we found that there are indications of the phase transition from a low density quasi-liquid phase to the high density symmetric phase of the Skyrmionic matter.