Fluid-magnet universality: Renormalization-group analysis ofφ5operators

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 ${\phi }^5$ addition to the usual ${\phi }^4$ theory. We show that no ${\phi }^5$ fixed point exists in the framework of an expansion around $d=\frac{10}{3}$. Further we show that to $O\left({\epsilon }_4^2\right)$, ${\epsilon }_4\equiv 4-d$, the ordinary ${\phi }^4$ fixed point is stable against the perturbations that mix with ${\phi }^5$. Two new correction-to-scaling exponents are found. One of the exponents, ${\Delta }_5$, is poorly determined with a range of values from 0.5 to 1.0 compatible with the $O\left({\epsilon }_4^2\right)$ result. However, its positivity rules out a separate fluid fixed point, indicating fluid-magnet asymptotic universality. The second exponent, ${\Delta }_3$, can be determined exactly: ${\Delta }_3=1-\alpha -\beta$. This implies the universal existence of a contribution to the fluid diameter scaling like the internal energy.