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Unformatted text preview: Physics 127B Homework Set 6: (due February 24) Problem 1: Coupling to a massless field Problem 3.5 in Kardar, Statistical Physics of Fields, p. 51. Problem 2: Two-dimensional Heisenberg Magnet This model consists of classical spins vector S i on a simple square lattice where the spins are of fixed length S but can point in any direction. The Hamiltonian is H =- J summationdisplay ( ij ) vector S i vector S j (1) where the sum runs over nearest neighbor pairs i,j and J > 0. a) Write down the Landau free energy density f ( vectorm,T ) for this phase transition with vectorm ( x ) the average spin per site over some coarse graining region at position x . (Here, you do not need to calculate the parameters microscopically, although you can in principle figure them out from the earlier homework problem on Heisenberg spins). What is the temperature dependence of the mean field value of m = | vectorm | near T c ?...
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