The gym and running both work well to escape for a bit. The gym at any Army base is similar enough to any civilian gym, so you might as well be back home when you're there. Running lets you take your mind off everything and just clear your head, only thinking of putting one foot in front of the other, instead of thinking about the work or school you might be missing out on.
Reading of course is a classic escapism method. You can read stories from home, the past, the future, etc., and just get lost in them instead of thinking of loved ones.
Sleeping works well too, though sometimes the dreams of home can be worse than the thoughts while you're awake.
Working productively has always been one of my personal favorite methods to killing time. Though by definition it keeps you concentrated on the deployment, it at least helps you forget about home.
There's millions of ways to forget about home, and the trick is to use enough of them to where your thoughts aren't focused on what you're missing.