This could be solved by keeping everybody in solitary confinement, but that's overly cruel. Instead, I'd propose splitting the prison into a whole bunch of separate units, each consisting of maybe a dozen prisoners, who would share facilities and never interact with prisoners outside their own unit. Every month, the units would be broken down and prisoners reassigned to different units, preferably arranged so that no prisoner would encounter the same fellow prisoner twice in one sentence. This way we could give prisoners enough social interaction to stop 'em going crazy while preventing them from ever constructing any more than the most rudimentary social structures.
Any downsides I'm not considering? I'm assuming that the whole thing could be accomplished without occupying any more space than the existing prison system, and hopefully with fewer guards.