Phase Transitions: A Challenge for Intertheoretic Reduction?

I analyze the extent to which classical phase transitions, both first order and continuous, pose a challenge for intertheoretic reduction. My contention is that phase transitions are compatible with a notion of reduction that combines Nagelian reduction and what Thomas Nickles called Reduction(2). I also argue that, even if the same approach to reduction applies to both types of phase transitions, there is a crucial difference in their physical treatment: in addition to the thermodynamic limit, in continuous phase transitions there is a second infinite limit involved, which marks an important difference in the reduction of first-order and continuous phase transitions.