Phys 583 Advanced Field Theory Solutions Problem Set No . 2 Rodrigo Soto - Garrido March 30 , 2014 1 Renormalization Group for the Ashkin - Teller Model
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〈~r,~r〉 σ(~r)σ(~r)τ(~r)τ(~r) (1) where 〈~r, ~r′〉 denotes nearest neighboring sites and K2 > 0 and K4 > 0 are two coupling constants. 1. (a) For K2 → ∞ the system tends to minimize the first term in Eq. (1). This is achivied when σ(~r)σ(~r) = τ(~r)τ(~r) = 1 which translates to σ(~r) = σ(~r) and τ(~r) = τ(~r) ∀ ~r. The ground state is then four-fold degenerate. The four states are given by: σ(~r) τ(~r) +1 +1 +1 -1 -1 +1 -1 -1 (b) For K4 → ∞ the system tends to minimize the second term in Eq. (1). In this case σ(~r)σ(~r)τ(~r)τ(~r) = 1 which is the same as σ(~r)τ(~r) = σ(~r)τ(~r) =⇒ σ(~r)τ(~r) = ±1 ∀ ~r. In this case the Hamiltonian (1) is given by: H =−K2 ∑
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Phys 583 Advanced Field Theory Solutions Problem Set No . 3 Rodrigo Soto - Garrido May 1 , 2014 1 Renormalization of an Interacting Field Theory of Fermions
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تاریخ انتشار 2014