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

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

1995-03-03

arxiv.org/abs/cond-mat/9503038v1

Phys.Lett. B342 (1995) 284-296

Physics

Condensed Matter

PostScript file

Scientific paper

10.1016/0370-2693(94)01377-O

The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-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 $N\geq3$, 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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