Exact Five-Loop Renormalization Group Functions of ${\varphi }^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$

Abstract

The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the ${\varphi }^4$-theory with two coupling constants associated with an $O(N)$-symmetric and a cubic interaction. Divergences are removed by minimal subtraction. The critical exponents $\eta$, $\nu$, and $\omega$ are expanded up to order ${\epsilon }^5$ for the three nontrivial fixed points O(N)-symmetric, Ising, and cubic. The results suggest the stability of the cubic fixed point for $N\ge 3$, implying that the critical exponents seen in the magnetic transition of three-dimensional cubic crystals are of the cubic universality class. This is in contrast to earlier three-loop results which gave $N>3$, and thus Heisenberg exponents. The numerical differences, however, are less than a percent making an experimental distinction of the universality classes very difficult.

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References in corpus (1)

• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

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