  Landau theory is used to investigate the behaviour of a metallic magnet
driven towards a quantum critical point by the application of pressure. The
observed dependence of the transition temperature with pressure is used to show
that the coupling of the magnetic order to the lattice diverges as the quantum
critical point is approached. This means that a first order transition will
occur in magnets (both ferromagnets and antiferromagnets) because of the
coupling to the lattice. The Landau equations are solved numerically without
further approximations. There are other mechanisms that can cause a first order
transition so the significance of this work is that it will enable us to
determine the extent to which any particular first order transition is driven
by coupling to the lattice or if other causes are responsible.
