Q: Is it possible to build muscle on a low carb diet like Atkins or South Beach?

A: Somebody just starting out with a below average or even an average physique will be able to put on muscle with almost any diet. After 6-12 months of progress though, you'd need to have caloric excess and slow weight gain in order to continue building muscle at appreciable rate. At this point, Atkins or South Beach will make it really difficult for you to keep gaining since they're designed specifically to prevent weight gains. South Beach, with large portion sizes in order to overeat, would be your best bet in this case. But it would still give inferior muscle-building results compared to higher-carb diet.

So, it is theoretically possible, but it wouldn't really provide any advantage over a more muscle-friendly bulking diet -- if you can gain weight and muscle on a certain diet, it means you'll likely gain some fat on it as well, regardless of whether it's South Beach or a traditional bulking diet.