  We have measured the specific heat of single crystals of the triple-layer
Ruddlesden-Popper material, Sr4Ru3O10, grown both in an image furnace and by
flux-growth. The flux grown sample has a sharp mean-field-like anomaly at the
onset of magnetic order, Tc = 102 K, but a much broader anomaly, indicative of
residual heterogeneity, is observed for the image furnace sample. Even for the
flux grown sample, however, the anomaly is at least an order of magnitude
smaller than one would expect for complete ordering of the spins. Neither
sample exhibits an anomaly at Tm ~ 50 K, where magnetic measurements suggest
that basal plane antiferromagnetism sets in. Anomalous behavior (e.g.
consistent with a term in the specific heat ~ T^3/2 as would be observed for a
three-dimensional ferromagnet with weak exchange) is observed at low
temperatures for both samples, indicative of the unusual magnetic order in this
material.
