Explaining universality: infinite limit systems in the renormalization group method

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable.

Automated summary

The author analyzes the role of infinite idealizations in the renormalization group method to explain universality in critical phenomena, arguing that infinite limit systems are not necessary for explaining universality. Introducing the linearization* property as a relevant factor in RG explanations, the author presents a proposition to support their view that infinite limit systems are dispensable.