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# p212ps4 - Physics 212 Statistical mechanics II Fall 2006...

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Unformatted text preview: Physics 212: Statistical mechanics II, Fall 2006 Problem set 4 : due 10/26/06 1. In class we showed that β = 1 / 4 in the mean-field theory of a tricritical point. Calculate the critical exponents γ, δ . The form of the Landau free energy per site for a tricritical point is f ( m ) = atm 2- hm + wm 6 , i.e., an additional experimental parameter has been used to tune the coefficient of m 4 to zero. Assuming that these values of β, γ, δ are correct in d = 3, what are the corresponding values of y t and y h ? To save you time, some useful relations from the scaling form in class are β = d- y h y t , γ = 2 y h- d y t , δ = y h d- y h . (1) Explain along which directions in the phase diagram of the Blume-Capel model (Lecture XV) you would expect to measure the exponents β, γ, δ . Note that there are three relevant directions rather than two, so there should be an additional fundamental exponent y 4 (related to the coefficient of the m 4 term) in addition to y t and y h , which we will calculate soon in...
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p212ps4 - Physics 212 Statistical mechanics II Fall 2006...

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