  The Moderate Deviations Principle (MDP) is well-understood for sums of
independent random variables, worse understood for stationary random sequences,
and scantily understood for random fields. Here it is established for
splittable random fields.
  Version 2. Adapted to new Version 3 of [2] arXiv:1706.00991. Terminology:
"CMS random fields". Numbers of items in [2] updated. References: "response",
not "responce". Otherwise unchanged.
