  We study the thermodynamics of asymmetric nuclear matter using a mean field
approximation with a Skyrme effective interaction, in order to establish its
phase diagram and more particularly the influence of isospin on the order of
the transition. A new statistical method is introduced to study the
thermodynamics of a multifluid system, keeping only one density fixed the
others being replaced by their intensive conjugated variables. In this ensemble
phase coexistence reduces to a simple one dimensional Maxwell construction. For
a fixed temperature under a critical value, a coexistence line is obtained in
the plane of neutron and proton chemical potentials. Along this line the grand
potential presents a discontinuous slope showing that the transition is first
order except at the two ending points where it becomes second order. This
result is not in contradiction with the already reported occurrence of a
continuous transformation when a constant proton fraction is imposed. Indeed,
the proton fraction being an order parameter in asymmetric matter, the
constraint can only be fulfilled by gradual phase mixing along the first-order
phase transition line leading to a continuous pressure.
