  In this paper, we are concerned with sample path properties of isotropic
spherical Gaussian fields on $\S^2$. In particular, we establish the property
of strong local nondeterminism of an isotropic spherical Gaussian field based
on the high-frequency behaviour of its angular power spectrum; we then exploit
this result to establish an exact uniform modulus of continuity for its sample
paths. We also discuss the range of values of the spectral index for which the
sample functions exhibit fractal or smooth behaviour.
