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Energy of chain of spins

  1. Oct 21, 2008 #1
    Hi all,

    I am supposed to calculate the energy of chain of spins where the magnetic field H = 0. For the first chain the spins are all aligned in the same direction - up - hence the energy

    U = -NJ

    where N is the total number of spins. Next, the half the chain is spin up and the other half is spin down with periodic boundary conditions first and last interact.

    UpUpUp....UpDownDown.....Down

    here I get the total energy U = -(N-2)*J but the book says -(N-4)*J which I really don't understand. Any comments appreciated - thanks in advance

    Best Jorgen
     
  2. jcsd
  3. Oct 22, 2008 #2

    alphysicist

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    Homework Helper

    Hi jorgen,

    I hope I am understanding the situation you describe, but the book answer makes sense to me. Each location of where there is an up-down neighbor represents an energy change (relative to the up-up or down-down case) of +2J (where J is the interaction energy magnitude between spin neighbors), because it goes from -J to +J. With the periodic boundary conditions, there are two of these locations.
     
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