Phase Transitions: A Challenge for Intertheoretic Reduction?

In this paper, I analyze the extent to which classical phase transitions, both first-order and continuous, pose a challenge for intertheoretic reduction. My main contention is that phase transitions are compatible with reduction, at least with a notion of inter-theoretic reduction that combines Nagelian reduction and what Nickles (1973) called reduction2. 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 fact, in addition to the thermodynamic limit, in the case of continuous phase transitions there is a second infinite limit involved that is related with the number of iterations in the renormalization group transformation. I contend that the existence of this second limit, which has been largely underappreciated in the philosophical debate, marks an important difference in the reduction of first-order and continuous phase transitions and also in the justification of the idealizations involved in these two cases.