Hidden superuniversality in systems with continuous variation of critical exponents

Abstract

Renormalization group theory allows continuous variation of critical exponents along a marginal direction (when there is one), keeping the scaling relations invariant. We propose a super universality hypothesis (SUH) suggesting that, up to constant scale factors, the scaling functions along the critical line must be identical to that of the base universality class even when all the critical exponents vary continuously. We demonstrate this in the Ashkin Teller (AT) model on a two-dimensional square lattice where two different phase transitions occur across the self-dual critical line: while magnetic transition obeys the weak-universality hypothesis where exponent ratios remain fixed, the polarization exhibits a continuous variation of all critical exponents. The SUH not only explains both kinds of variations observed in the AT model, it also provides a unified picture of continuous variation of critical exponents observed in several other contexts.