Continuously Varying Critical Exponents Beyond Weak Universality

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${}_3$ $(0.5\le y\le 1)$ 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.

5 pages, 3 eps figures (and supplemental material 1 page, 2 eps figures)