  We describe how we have used simultaneously ${\cal O}(10^3)$ nodes of the
EGEE Grid, accumulating ca. 300 CPU-years in 2-3 months, to determine an
important property of Quantum Chromodynamics. We explain how Grid resources
were exploited efficiently and with ease, using user-level overlay based on
Ganga and DIANE tools above standard Grid software stack. Application-specific
scheduling and resource selection based on simple but powerful heuristics
allowed to improve efficiency of the processing to obtain desired scientific
results by a specified deadline. This is also a demonstration of combined use
of supercomputers, to calculate the initial state of the QCD system, and Grids,
to perform the subsequent massively distributed simulations. The QCD simulation
was performed on a $16^3\times 4$ lattice. Keeping the strange quark mass at
its physical value, we reduced the masses of the up and down quarks until,
under an increase of temperature, the system underwent a second-order phase
transition to a quark-gluon plasma. Then we measured the response of this
system to an increase in the quark density. We find that the transition is
smoothened rather than sharpened. If confirmed on a finer lattice, this finding
makes it unlikely for ongoing experimental searches to find a QCD critical
point at small chemical potential.
