= Spin-mixture contribution to zero-field susceptibility
{title2=$\chi_N\sim\beta_{\rm th}N M_0^2$}
In a symmetric equal mixture of two ordered <pure thermodynamic phases> with magnetizations $\pm M_0$, the mean spin vanishes but the large-distance two-spin expectation tends to $M_0^2$. Thus the <connected correlation function> of the mixture has a nondecaying part. The <correlation-function susceptibility sum rule> gives an extensive contribution $\beta_{\rm th}N M_0^2$ to susceptibility per spin. This is phase-switching response, not the connected susceptibility within one pure phase. The latter uses the thermodynamic limit followed by a one-sided zero-field limit, and subtracts the nonzero pure-phase mean before defining the <correlation length>.
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