The Ising magnetization exponent on Z² is 1/15

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We prove that for the Ising model defined on the plane ² at β=βc, the average magnetization under an external magnetic field h>0 behaves exactly like σ₀ᵦc, ₕ h 1 15. The proof, which is surprisingly simple compared to an analogous result for percolation (i.e. that θ(p)=(p-pc)⁵/³⁶⁺ᵒ⁽¹⁾ on the triangular lattice,) relies on the GHS inequality as well as the RSW theorem for FK percolation from. The use of GHS to obtain inequalities involving critical exponents is not new; in this paper we show how it can be combined with RSW to obtain matching upper and lower bounds for the average magnetization.