The concept of quantum criticality is proving to be central to attempts to
understand the physics of strongly correlated electrons. Here, we argue tha
t observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence
for a new class of quantum critical point, arising when the critical end p
oint terminating a tine of first-order transitions is depressed toward zero
temperature. This is of interest both in its own right and because of the
convenience of having a quantum critical point for which the tuning paramet
er is the magnetic field. The relationship between the resultant critical f
luctuations and novel behavior very near the critical field is discussed.