Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study

Abstract

We analyze the critical behavior of isotropic systems with dipole-dipole interaction by renormalization-group methods in fixed space-time dimensions. Working in three-dimensional theory we analytically find three-loop expressions for critical exponents in the limit of dominating dipole-dipole forces. Resummation of the series obtained provides numerical values close to $O(3)$-theory predictions, justifying the applicability of such a simplified model to systems with strong dipole-dipole interaction.

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• Stability of ${\phi }^4$-vector model: four-loop $\epsilon$ expansion study