Ferromagnetic instabilities in neutron matter at finite temperature with the Skyrme interaction

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The properties of spin polarized neutron matter are studied both at zero and finite temperature using Skyrme-type interactions. It is shown that the critical density at which ferromagnetism takes place decreases with temperature. This unexpected behaviour is associated to an anomalous behaviour of the entropy which becomes larger for the polarized phase than for the unpolarized one above a certain critical density. This fact is a consequence of the dependence of the entropy on the effective mass of the neutrons with different third spin component and a new constraint on the parameters of the effective Skyrme force is derived in order to avoid such a behaviour.