We discuss the thermodynamics of gluons in the background of static quark s
ources. In order to do so we formulate the quenched limit of QCD at non-zer
o baryon number. A first numerical analysis of this system shows that it un
dergoes a smooth deconfining transition. We find evidence for a region of c
oexisting phases that becomes broader with increasing baryon number density
. Although the action is in our formulation explicitly Z(3) symmetric the P
olyakov loop expectation value becomes non-zero already in the low temperat
ure phase. It indicates that the heavy quark potential stays finite at larg
e distances, i.e. the string between static quarks breaks at non-zero baryo
n number density already in the hadronic phase. (C) 1999 Published by Elsev
ier Science B.V. All rights reserved.