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Band correlative ferromagnetism-magnetism of conductive electrons in magnetic field

  1. Aug 9, 2011 #1
    HI!

    Also:

    I have 1-d electron gas in tight banding model with included interaction between electrons of same spins V[itex]_{\uparrow}[/itex]=-N[itex]_{\uparrow}[/itex]U where U > 0, [itex]\sigma[/itex]=[itex]\pm1[/itex] is spin up or down, and pauli interaction with outside field B is included. I have to calculate the total energy of gas at T=0K as function of of polarization x=[itex]\frac{N_{\uparrow}-N_{\downarrow}}{N}[/itex] expand it to series up to 6th order, minimize it and find the nontrivial solution for U


    [itex]N=N_{\uparrow}+N_{\downarrow}, N_{\uparrow}=\frac{N}{2}(1+x)[/itex]
    and [itex]N_{\downarrow}=\frac{N}{2}(1-x)[/itex]

    [itex]N_{\sigma}=\frac{N}{2}(1+{\sigma}x)[/itex]
    my major problem is calculating the total energy
     
    Last edited: Aug 9, 2011
  2. jcsd
  3. Aug 9, 2011 #2
    HI!

    My problem is next:

    I have 2-d electron gas with included interaction between electrons of opposite spins V[itex]_{\sigma}[/itex]=N[itex]_{\sigma}[/itex]U where U > 0 and [itex]\sigma[/itex]=[itex]\pm1[/itex] is spin up or down, and pauli interaction with outside field B is included. I have to calculate the total energy of gas at T=0K as function of N[itex]_{\sigma}[/itex], then i have to minimize the energy as function of polarization parameter x=[itex]\frac{N_{\uparrow}-N_{\downarrow}}{N}[/itex] and calculate the suscepitibility

    [itex]N=N_{\uparrow}+N_{\downarrow}, N_{\uparrow}=\frac{N}{2}(1+x)[/itex], [itex]N_{\downarrow}=\frac{N}{2}(1-x), and N_{\sigma}=\frac{N}{2}(1+{\sigma}x) [/itex]

    my major problem is calculating the total energy, the rest is not so tough i am just not sure that my energy is calculated correct.......
     
    Last edited: Aug 9, 2011
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