Avoiding contact is not just a passive-aggressive way to make your ex miss you. It gives you time to do the things you need to do to prepare yourself for a new relationship (whether it's with your ex or someone new!). Take time during this month to get to know yourself as an individual and to work on areas that you may have let slip during your relationship with your ex. If you contributed to the breakup, this is the time to pinpoint your relationship weaknesses and do the hard work to improve as a human being.
In the dating world, I often see that one of the most common reasons men pull away is that they find the woman to be challenging, and she gives in because she likes him. She starts settling and making excuses for his lazy or inappropriate behavior. There are many times I see a woman dating a man, and he shows all the signs that he is not ready for a relationship with his behavior and his words. Instead of pushing yourself towards him in the hopes of changing his mind, I believe the right thing to do in this situation is to dig deep into your feelings. If you can control your feelings by maintaining a friendship, then go for it. (And I’m not talking about being “friends with benefits.”)