Hidden superuniversality in systems with continuous variation of critical exponents

TL;DR

This paper proposes a super universality hypothesis suggesting that critical scaling functions remain invariant along a critical line, even when critical exponents vary continuously, as demonstrated in the Ashkin Teller model.

Contribution

The paper introduces the super universality hypothesis and demonstrates its validity in the Ashkin Teller model, unifying different types of critical exponent variations.

Findings

Scaling functions are identical up to scale factors along the critical line.

The Ashkin Teller model exhibits both fixed and continuously varying critical exponents.

The hypothesis explains diverse critical behaviors in various systems.

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.