Continuously Varying Critical Exponents Beyond Weak Universality

TL;DR

This paper reports a ferromagnetic phase transition where all critical exponents vary with composition, violating weak universality, and introduces a new scaling theory that explains this phenomenon and generalizes to multicriticality.

Contribution

It presents experimental evidence of all critical exponents varying in a phase transition, challenging existing universality concepts, and proposes a new scaling theory encompassing these findings.

Findings

All critical exponents vary with composition y.

The variation violates both universality and weak universality.

A new scaling theory explains the continuous variation and multicriticality.

Abstract

Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., $\beta, \gamma, \nu$) vary keeping others (e.g., $\delta , \eta$) fixed. Here we report a ferromagnetic phase transition in (Sm$_{1-y}$Nd$_{y}$)$_{0.52}$Sr$_{0.48}$MnO$_3$ $(0.5\le y\le1)$ single crystal where all critical exponents vary with $y.$ Such variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multicriticality.