please use python and provide the codes According to mean-field theory of ferromagnetism, strength of magnetization M of a ferromagnetic material such as iron, depends on the temperature T as stated in M = u tanh MJ TKB where u is magnetic moment, kg is Boltzmann's constant and J is coupling constant. After simplifying this equation, x = tanh where x = M and C = ". kB Magnetization x (in units of µ) could be solved with relaxation method. Denote x after i iterations as x; (initial guess as xo) Plot the actual error |x – x*| for relaxation method and for over-relaxation method (with w = 1) in the same figure. Estimate r using 50 iterations in the over-relaxation method. Use C=1, T=0.9 and xo = 1. x* is the accurate solution

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please use python and provide the codes
According to mean-field theory of ferromagnetism, strength of magnetization M of a ferromagnetic material
such as iron, depends on the temperature T as stated in M = µ tanh
where u is magnetic moment, kg is Boltzmann's constant and J is coupling constant.
After simplifying this equation, x = tanh
where x =
T
and C =
kB
Magnetization x (in units of µ) could be solved with relaxation method.
Denote x after i iterations as x¡ (initial guess as xX0).
Plot the actual error |x – x*| for relaxation method and for over-relaxation method (with
w = 1) in the same figure. Estimate x* using 50 iterations in the over-relaxation method.
Use C=1, T=0.9 and xo = 1.
x* is the accurate solution
Transcribed Image Text:please use python and provide the codes According to mean-field theory of ferromagnetism, strength of magnetization M of a ferromagnetic material such as iron, depends on the temperature T as stated in M = µ tanh where u is magnetic moment, kg is Boltzmann's constant and J is coupling constant. After simplifying this equation, x = tanh where x = T and C = kB Magnetization x (in units of µ) could be solved with relaxation method. Denote x after i iterations as x¡ (initial guess as xX0). Plot the actual error |x – x*| for relaxation method and for over-relaxation method (with w = 1) in the same figure. Estimate x* using 50 iterations in the over-relaxation method. Use C=1, T=0.9 and xo = 1. x* is the accurate solution
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