They Ran Away

What Hawk found in the Frost Giant city was not at all what anyone had been expecting. The city itself was nearly demolished, with a large breach in the wall that faced the Ash Wastes near the volcano. 

He was not the first one there, the Elementals had beat him to it, and from the look of it, they had either taken the city or done enough damage to make the civilian population retreat. There was still a sizeable military contingent nearby, so the Elementals might not have won the battle, but the city was demolished anyhow.

That began a search for the summoning spot. If he could find that, they could smash it and stop the reinforcements entirely. There was nobody on this team who wanted to leave more than Hawk did, and that included Remi, who couldn't survive the cold for long in her current state.

The logical place for him to start was where the remaining Giants were. If they were still being summoned, the stones had to be there.