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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 = 1 / 4 in the mean-field theory of a tricritical point. Calculate the critical exponents , . 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 , , 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 = d- y h y t , = 2 y h- d y t , = 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 , , . 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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