  We derive a set of isometric fluctuation relations, which constrain the order
parameter fluctuations in finite-size systems at equilibrium and in the
presence of a broken symmetry. These relations are exact and should apply
generally to many condensed-matter physics systems. Here, we establish these
relations for magnetic systems and nematic liquid crystals in a
symmetry-breaking external field, and we illustrate them on the Curie-Weiss and
the $XY$ models. Our relations also have implications for spontaneous symmetry
breaking, which are discussed.
