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Homework Help: Three magnetic systems in thermal contact

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    "Consider three magnetic systems in thermal contact, each composed of N1, N2, N3 spins, +m or -m. Starting from s1 = s'1 + δ1 etc. calculate the average square deviation <si2 of each system.

    2. Relevant equations

    s'1 is the most probable configuration for s1. N1+N2+N3 = N ; s1+s2+s3 = s

    3. The attempt at a solution

    I have multiplied each multiplicity function; g1(N1,s1).g2(N2,s2).g3(N3,s3) = g1g2g3exp{-(2s12/N1)-(2s22/N2) - (2s32/N3)}

    then i wrote s3 = s - s1 -s2

    Then i took log of the equation from both side and took derivative with respect to s1 and s2 and set s1=s'1, s2=s'2. They have to be equal to zero since it is extremum.

    I came to this point and i couldn't do anything more.
  2. jcsd
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