# Isothermal Magnetic Susceptibility

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 P: 916 My book says that "in the mean field approximation, the isothermal magnetic susceptibility just below the Curie temperature goes as ##(T_c-T)^{-1}##". I need some help understanding how to get this proportionality. My book does not contain any derivation or further explanations. According to my notes the isothermal magnetic susceptibility ##\chi_T## diverges near ##T_c##: ##\chi_T = \frac{\partial M}{\partial H} |_T## Differentiating the equation of state we get: ##\frac{1}{k_B T} = \chi_T (1- \tau) +3M_s^2 \chi_T \left( \tau - \tau^2 + \frac{\tau^3}{3} \right)## Where ##\tau=T_c/T##. If Ms=0 we get: ##\chi_T = \frac{1}{k_B}\frac{1}{T-T_c}## But how do we get ##T_c - T## in the denominator? We need ##\chi_T \propto (T_c-T)^{-1}## NOT ##(T-T_c)^{-1}##. Also are we justified to set magnetization to 0 for ##TT_c##. Any explanation is greatly appreciated.
 P: 1,970 Can you show the equation of state? Something is not right. If τ=Tc/T, at T
 P: 916 Thank you for your response. Unfortunately that information is not provided. So how else can we demonstrate that magnetic susceptibility is inversely proportional to (Tc-T)?

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