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We are concerned with sample path properties of isotropic sphericalGaussian fields on the unit sphere.In particular,we establish the property of strong localnondeterminism of an isotropic spherical Gaussian field based on the high-frequencybehaviour of its angular power spectrum; we then exploit this result to establishan exact uniform modulus of continuity for its sample paths.We also discuss therange of values of the spectral index for which the sample functions exhibit fractalor smooth behaviour.