the exhausted just ＝ the completely tired body?

Context:

It was a hard day's run, up the Canyon, through Sheep Camp, past the Scales and the timber line, across glaciers and snowdrifts hundreds of feet deep, and over the great Chilcoot Divide, which stands between the salt water and the fresh and guards forbiddingly the sad and lonely North. They made good time down the chain of lakes which fills the craters of extinct volcanoes, and late that night pulled into the huge camp at the head of Lake Bennett, where thousands of gold-seekers were building boats against the breakup of the ice in the spring. Buck made his hole in the snow and slept the sleep of the exhausted just, but all too early was routed out in the cold darkness and harnessed with his mates to the sled.

More:

http://london.sonoma.edu/Writings/CallOfTheWild/chapter2.html