Continuously Varying Critical Exponents Beyond Weak Universality

Abstract

Renormalization group theory does not restrict the form 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., β, γ, ν) vary keeping others (e.g., δ, η) fixed. Here we report ferromagnetic phase transition in (Sm1−yNdy)0.52Sr0.48MnO3 (0.5 ≤ y ≤ 1) single crystals where all three exponents β, γ, δ vary with Nd concentration y. Such a 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 multi-criticality.

Adsorption of flexible polymer chains on a surface: Effects of different solvent conditions

“…Still within the scope of universality, since the exponents should be equal for s = 0, such behavior seems to violate both universality and weak universality hypotheses (as is well known, in the weak universality the exponents vary but their ratio is constant). This kind of violation of both hypothesis has been recently reported for the ferromagnetic phase transition of (Sm 1−y Nd y ) 0.52 Sr 0.48 MnO 3 single crystals with (0.5 ≤ y ≤ 1), where the magnetic exponents vary with Nd concentration y [34]. Our polymer adsorption model can be seen as a similar example of such new scaling behavior, providing also a generic route leading to continuous variation of critical exponents and multi-criticality.…”

DNA melting in poor solvent

“…In the study of critical phenomena, a continuous variation of the exponents, often induced by a marginal interaction in the RG sense, is rarely observed [23,24]. For the unperturbed case, the two universality classes for melting, using PS and alike models, is for ideal random walk (φ = 1/2 and continuous melting) and for self-avoiding walk (φ = 1 and first-order melting).…”

Full nonuniversality of the symmetric 16-vertex model on the square lattice

“…Weak universality was observed in many two-dimensional (2D) systems, including the Ashkin-Teller model [6][7][8], absorbing phase transitions [9], the spin-1 Blume-Capel model [10], frustrated spin models [11,12], percolation models [13], etc. There are few exceptions from models with continuously varying critical exponents which violate weak universality, such as micellar solutions [14], Ising spin glasses [15], itinerant composite magnetic materials [16,17], etc. The partition function of the "electric" 8-vertex model on the square lattice can be mapped onto the partition function of a "magnetic" Ising model on the dual (also square) lattice with nearest-neighbor two-spin and plaquette four-spin interactions [18,19].…”