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The electronic excitations at the edges of a Hall bar not much wider than afew magnetic lengths are studied theoretically at filling $\nu = 2$. Bothmean-field theory and Luttinger liquid theory techniques are employed for thecase of a null Zeeman energy splitting. The first calculation yields a stablespin-density wave state along the bar, while the second one predicts dominantWigner-crystal correlations along the edges of the bar. We propose anantiferromagnetic Wigner-crystal groundstate for the edge electrons thatreconciles the two results. A net Zeeman splitting is found to produce cantingof the antiferromagnetic order.Comment: 22 pgs. of PLAIN TeX, 1 fig. in postscript, published versio

physical review. b, condensed matter

Wigner crystal state for the edge electrons in the quantum Hall effect at filling<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>

Wigner crystal state for the edge electrons in the quantum Hall effect at fillingν=2