2025/10/26 by Grocholski, Oskar, Chankowski, Piotr H.
#FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas)
paper · doi:10.48550/arxiv.2510.22719
In the previous work we have developed a systematic thermal (imaginary time) perturbative expansion and applying it to the relevant effective field theory computed, up to the second order in the interaction, the free energy F of the diluted gas of (nonrelativistic) spin 1/2 fermions interacting through a spin-independent repulsive two-body potential. Here we extend this computations to higher orders: assuming that the only relevant parameter specifying the interaction potential is the s-wave scattering length a0, we compute the complete order (k\rm Fa0)3 (k\rm F is the Fermi wave vector) contribution to the system's free energy as a function of the numbers N+ and N- of spin up and spin down fermions (i.e. as a function of its polarization) and the temperature T. We also extend the computation beyond a fixed order by resumming the contributions to F of two infinite sets of Feynman diagrams: the so called particle-particle rings and the particle-hole rings. We find that including the second one of these two contributions has a dramatic consequence for the transition of the system from the paramagnetic to the ferromagnetic phase (the so called Stoner phase transition): in this approximation the phase transition simply disappears.