Fluid-magnet universality: Renormalization-group analysis of φ5 operators

Abstract

The question of a possible difference between the universality classes of fluids and Ising-like magnets is addressed by perturbation theory and the renormalization group. The most dangerous possibility is that of an φ5 addition to the usual φ4 theory. We show that no φ5 fixed point exists in the framework of an expansion around d=10/3. Further we show that to O(ε2/4), ε4≡4−d, the ordinary φ4 fixed point is stable against the perturbations that mix with φ5. Two new correction-to-scaling exponents are found. One of the exponents, Δ5, is poorly determined with a range of values from 0.5 to 1.0 compatible with the O(ε2/4) result. However, its positivity rules out a separate fluid fixed point, indicating fluid-magnet asymptotic universality. The second exponent, Δ3, can be determined exactly: Δ3=1−α−β. This implies the universal existence of a contribution to the fluid diameter scaling like the internal energy.