Critical endpoint and universality class of neutron $^3P_2$ superfluids in neutron stars

TL;DR

This paper investigates the critical phenomena and phase transitions of neutron $^3P_2$ superfluids in neutron stars, revealing a new universality class at the critical endpoint and demonstrating the effectiveness of high-order Ginzburg-Landau theory.

Contribution

It identifies a new universality class at the critical endpoint of phase transitions in neutron $^3P_2$ superfluids and validates the high-order Ginzburg-Landau theory for describing critical behavior.

Findings

Critical exponents at the CEP satisfy Rushbrooke, Griffiths, and Widom equalities.

Phase diagram includes uniaxial/biaxial nematic, ferromagnetic, and cyclic phases.

High-order Ginzburg-Landau theory accurately captures critical phenomena at the CEP.

Abstract

We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (CEP). We demonstrate that the set of critical exponents at the CEP satisfies the Rushbrooke, Griffiths, and Widom equalities, indicating a new universality class. At the CEP, the $^3P_2$ superfluid exhibits critical behavior with nontrivial critical exponents, indicating a new universality class. Furthermore, we find that the Ginzburg-Landau (GL) equation up to the 8th-order expansion satisfies three equalities and properly captures the physics of the CEP. This implies that the GL theory can provide a tractable way for understanding critical phenomena which may be realized in the dense core of realistic magnetars.