How to model macroscopic worlds : towards the philosophy of condensed matter physics
Condensed matter physics studies many-body phenomena, the phenomena involving a huge number of constituents interacting with each other strongly. My theme is modelling in condensed matter physics: the construction of mathematical/physical structures in order to understand many-body phenomena in the world. I study how condensed matter physicists learn about many-body phenomena from the successful employment of models. My proposal is to construe condensed matter physics as engaged essentially with the three activities: model-building, model-exploring and model-based understanding. General theories such as statistical mechanics guide the process of model-building as model-building methodology. I discuss the multiple layers of interactions among general theories (particularly among thermodynamics and statistical mechanics) and show that complementation and cooperation rather than reduction are better concepts for understanding their relation. In model-exploring stage, we probe a model in order to determine what exactly the model implies in itself and what it could with additional constraints. I investigate a number of epistemic roles of approximations in this stage. I also discuss what consists of model-based understanding. With the help of appropriate interpretative models, an well-understood model can provide us with our best representation of the phenomena (substantial theories). Finally, I investigate how physicists successfully deal with some crucial features of critical phenomena using renormalization group methods. I compare the renormalization group methods of condensed matter physics with those of quantum field theory, and argue. I claim that the mean field methods and renormalization group methods in condensed matter physics complement to each other.