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The local field will vary from nuclues to nucleus, slightly
changing the Larmor frequencies of each.

[Diagram of 6 dots arrranged in a circle with one dot in the center labeled ith. An arrow is drawn from the central dot to the dot to its upper left.]
Distances between the nuclei fixed.
Geometrical configuration fixed
* spin configuration may be different
at different time.

At the i^th nucleus, let us suppose for simplicity that
the neighboring nuclei have spin I = 1/2. Each of them can
be parallel or antiparallel to H₀. For each spin configuration
we have a definite value of the z-component of the local field.
Let us first consider only the nearest neighbors. Instead of one
value H₀, we have e.g. ten possible values around H₀, depending
which neighbors are parallel & which antiparallel to H₀. Now
all the configurations of the next nearest neighbors will split
each of the ten values into many more, and so on for the third
nearest, etc. The result will be a continuum of values of the
z-component of the local field & therefore a distribution over a
range of Larmor frequencies.