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

Strong Local Nondeterminism and Exact Modulus of Continuity for Spherical Gaussian Fields