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Phase Transitions Questions and Answers

1.

According to Weiss molecular theory near the critical point the isothermal susceptibility of the magnetic system behaves as :

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

Near the critical point \(\chi_{T} \propto |T - T_{C}|^{-1}\).

In Weiss's molecular field theory each spin feels the applied field plus an internal field proportional to the magnetisation. Solving self-consistently above \(T_{C}\) gives the Curie-Weiss law:

\[ \chi = \frac{C}{T - T_{C}} \]

So the susceptibility diverges with critical exponent \(\gamma = 1\), the mean-field value. The exponent 1/2 belongs to the magnetisation below \(T_{C}\) (\(M \propto (T_{C} - T)^{1/2}\), \(\beta = 1/2\)), not the susceptibility, and a positive power would make \(\chi\) vanish at the critical point instead of diverging.

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