EFT as a gas of random walks with hard-core interactions

Abstract

We are now ready to set the stage for Parts II and III of this book. The method exploited in this book consists in representing spin systems in terms of interacting random walks We can then use geometrical arguments to derive properties of these random walks, which in turn imply differential inequalities for the corresponding spin systems. These derivations are the subject of Part II of the book. The inequalities have a number of consequences for the critical behavior of the system and the nature of the continuum limit These consequences are detailed in Part III of the book (which can be read independently of Part II).