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matematikuvol
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Zero field magnetisation like a function of temperature vanished in ##T=T_c## as ##(T_c-T)^{\beta}##. Let ##M_1## be a magnetisation for temperature ##T_1##. Since ##\forall M<M_1##, ##(\frac{\partial A}{\partial M})_T=H=0## it follows that
[tex]A(T_1,M)=A(T_1,0)[/tex] for ##M \leq M_1(T_1)##
Why only for ##M \leq M_1(T_1)##?
Now define the function
[tex]A^{*}(T,M)=\{A(T,M)-A_c\}+(T-T_c)S_c[/tex]
[tex]S^{*}(T,M)=S(T,M)-S_c[/tex]
So ##S^{*}(T,M)=-(\frac{\partial A^{*}}{\partial T})_M##
Now in Griffiths construction I need to drive a tangent in point ##T=T_1##. Eq of tangent is
[tex]f(T)=A^{*}(T_1,M_1)+(T-T_1)(\frac{\partial A^{*}}{\partial T})_{T=T_1}[/tex]
I can't visualise this.
[tex]A(T_1,M)=A(T_1,0)[/tex] for ##M \leq M_1(T_1)##
Why only for ##M \leq M_1(T_1)##?
Now define the function
[tex]A^{*}(T,M)=\{A(T,M)-A_c\}+(T-T_c)S_c[/tex]
[tex]S^{*}(T,M)=S(T,M)-S_c[/tex]
So ##S^{*}(T,M)=-(\frac{\partial A^{*}}{\partial T})_M##
Now in Griffiths construction I need to drive a tangent in point ##T=T_1##. Eq of tangent is
[tex]f(T)=A^{*}(T_1,M_1)+(T-T_1)(\frac{\partial A^{*}}{\partial T})_{T=T_1}[/tex]
I can't visualise this.