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We investigate the low energy properties of Lorentz-invariant theories with aspontaneously broken rotation symmetry O(N) $\to$ O(N--1). The leadingcoefficients of the low temperature expansion for the partition function arecalculated up to and including three loops. Emphasis is put into the specialcase N=3: it describes the antiferromagnet which has been extensively studied.Our results obtained within the framework of the effective Lagrangian techniqueare compared with the literature. In particular, we show that, at order $T^7$for the heat capacity and $T^6$ for the order parameter, respectively,logarithmic terms appear in the low temperature expansion, which have beenoverlooked so far.Comment: Published versio

physical review. b, condensed matter

Effective analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">O</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>antiferromagnet: Low-temperature expansion of the order parameter

Effective analysis of theO(N)antiferromagnet: Low-temperature expansion of the order parameter