  The Zamolodchikov's conjecture implying the exceptional Lie group E8 seems to
be validated by an experiment on the quantum phase transitions of the 1D Ising
model carried out by the Coldea et. al. The E8 model which follows from the
affine Toda field theory predicts 8 bound states with the mass relations in the
increasing order m1, m2= tau m1, m3, m4, m5, m6=tau m3, m7= tau m4, m8= tau m5,
where tau= (1+\sqrt(5))/2 represents the golden ratio. Above relations follow
from the fact that the Coxeter group W(H4) is a maximal subgroup of the
Coxeter-Weyl group W(E8). These masses turn out to be proportional to the radii
of the Gosset's circles on the Coxeter plane obtained by an orthogonal
projection of the root system of E8 . We also note that the masses m1, m3, m4
and m5 correspond to the radii of the circles obtained by projecting the
vertices of the 600-cell, a 4D polytope of the non-crystallographic Coxeter
group W(H4). A special non-orthogonal projection of the simple roots on the
Coxeter plane leads to exactly the numerical values of the masses of the bound
states as 0.4745, 0.7678, 0.9438, 1.141, 1.403, 1.527, 1.846, and 2.270. We
note the striking equality of the first two numerical values to the first two
masses of the bound states determined by the Coldea et. al.
