Federico Camia, Christophe Garban, Charles M. Newman
In this paper, we prove that for the Ising model defined on the plane $\Z^2$ at $\beta=\beta_c$, the average magnetization under an external magnetic field $h>0$ behaves exactly like $<{\sigma_0}_{\beta_c, h} \asymp h^{1/15}.$ The proof, which is surprisingly simple compared to an analogous result for percolation (i.e. that $\theta(p)=(p-p_c)^{5/36+o(1)}$ on the triangular lattice \cite{\SmirnovWerner,\KestenScaling}) relies on the GHS inequality.
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http://arxiv.org/abs/1205.6612
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