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

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