The phase diagram of 2D polar condensates in a magnetic field

TL;DR

This paper maps out the phase diagram of 2D polar spin-1 condensates under magnetic fields, revealing multiple phase transitions including Ising and Kosterlitz--Thouless types, with transitions merging at high Zeeman strengths.

Contribution

It provides the first detailed phase diagram of 2D polar condensates in magnetic fields, identifying the nature and interplay of multiple phase transitions.

Findings

Identification of Ising and KT transitions in the phase diagram.

Transitions merge at high Zeeman fields.

Monte Carlo simulations confirm the phase structure.

Abstract

Spin one condensates in the polar (antiferromagnetic) phase in two dimensions are shown to undergo a transition of the Ising type, in addition to the expected Kosterlitz--Thouless (KT) transition of half vortices, due to the quadratic Zeeman effect. We establish the phase diagram in terms of temperature and the strength of the Zeeman effect using Monte Carlo simulations. When the Zeeman effect is sufficiently strong the Ising and KT transitions merge. For very strong Zeeman field the remaining transition is of the familiar integer KT type.