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In Advanced topic in quantum field theory / M. Shifman on page 251 the author discusses the fact that the theta term is topological and does not affect the equations of motion. Then he said:

"In particular, at $\theta=\pi$ the O(3) sigma model becomes conformal and describes a ferromagnet rather than antiferromagnet. Unfortunately, I cannot dwell on the aspect in this text"

Where he refers to the term $\frac{\theta}{8\pi}S^{a}(\partial_{\mu}S^{b})(\partial_{\nu}S^{c})\varepsilon^{\mu\nu}\varepsilon_{abc}$.

I would like to see here more details about this point. Is it a uniqe phenomena for $\theta=\pi$?

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