We study a multi-matrix model whose low temperature phase is a
fuzzy sphere that undergoes an evaporation transition as the temperature
is increased. We investigate finite size scaling of the system as the limiting
temperature of stability of the fuzzy sphere phase is approached. We find
on theoretical grounds that the system should obey scaling with specific
heat exponent = 1
2 , shift exponent = 4
3 and that the peak in the
specific heat grows with exponent ! = 2
3 . Using hybrid Monte Carlo
simulations we find good collapse of specific heat data consistent with a
scaling ansatz which give our best estimates for the scaling exponents as
= 0.50 ± 0.01, = 1.41 ± 0.08 and ! = 0.66 ± 0.08
