Universality Explained

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Franklin, Alexander
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It is commonly claimed, both by physicists and philosophers that the universality of critical phenomena is explained through particular applications of the Renormalisation Group (RG). This paper seeks to clarify this explanation. The derivation of critical exponents proceeds in two ways: (i) via a real-space and (ii) via a momentum-space application of the RG. Following Mainwood (2006) I argue that these approaches ought to be distinguished: while (i) fails adequately to explain universality, (ii) succeeds in the satisfaction of this goal. (i) depends on various extensions to the Ising model. These serve as archetypes of the different universality classes. I emphasise that the derivation does not take diverse systems and justify their inclusion in each universality class, rather universality is assumed and the critical exponents are obtained for each class from its archetype alone. (ii) starts with an effective Hamiltonian which abstracts away from the details of different physical systems. It can be shown that the addition of various operators to this Hamiltonian would be irrelevant to the derived values of the critical exponents; this implies that multiple Hamiltonians belong to the same universality class. As such, universality is explained by the general applicability of the effective Hamiltonian. I further claim that we have good reason to believe that a reductive explanation of universality could be formulated; this follows from the explanatory strategy clarified in previous sections. I argue that the possibility of a reductive explanation undermines claims in Batterman (2014) and Morrison (2014) that the RG explanation of universality is irreducible. In addition, this may provide a paradigm example of a reductive explanation of multiple realisability.