For the ferromagnets EuS and GdMg, in which fourth-order exchange interacti
ons (i.e. biquadratic, three-spin and four-spin interactions) have been ide
ntified, the deviation of the spontaneous magnetization with respect to the
T = 0 value is shown to follow a T-2 law instead of the famous T-3/2 law e
xpected for a Heisenberg ferromagnet. Moreover, the observed T2 law holds f
or temperatures as large as 0.8T(c) and the extrapolated magnetization valu
e for T --> 0 does not conform to ferromagnetic saturation. This is because
the fourth-order exchange interactions generate a second order-parameter w
hich is assumed to govern the order of the transverse moment components. Th
ese moment components have a finite expectation value for T --> 0 at the ex
pense of the Heisenberg order parameter. Like the spontaneous magnetization
, the critical field curves B-c(T) of the metamagnet EuSe and the antiferro
magnet EuTe also start decreasing with a T-2 term for T --> 0. It is argued
that the T-2 law is a consequence of the fourth-order exchange interaction
s. This is shown experimentally by a study of the critical field curves B-c
(parallel to)(T --> 0) pertinent to the longitudinal (Heisenberg) order-par
ameter in the diamagnetically diluted antiferromagnets EuxSr1-xTe. In this
solid solution series a particular composition of x(c) = 0.85 exists at whi
ch the different fourth-order interaction processes compensate each other i
n the high temperature average. As a consequence, an EuxSr1-xTe sample with
x = 0.85 meets the requirements of a Heisenberg antiferromagnet at least i
f a quantity is considered for which the high-temperature average over all
fourth-order interactions is decisive. This seems to be the case for the cr
itical field curve B-c(parallel to)(T --> 0) which gives the phase boundary
to the paramagnetic phase. In fact, a crossover from a T-2 to a T-3/2 law
is observed for B-c(parallel to)(T --> 0) on approaching x(c). This, we bel
ieve, shows the frequently observed T2 law is caused by the fourth-order in
teractions.