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Questions and Answers > Transfer Matrices & Position space renormalization

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The spin–1 model: Consider a linear chain where the spin si at each site takes on three values si = -1, 0, +1. The spins interact via a Hamiltonian 2. Clock model: Each site of the lattice is oc ... cupied by a q-valued spin si ≡ 1, 2, · · ·, q, with an underlying translational symmetry modulus q, i.e. the system is invariant under si → (si + n)modq. The most general Hamiltonian subject to this symmetry with nearest– neighbor interactions is 3. XY model: Consider two component unit spins ~si = (cos θi, sin θi) in one dimension, with the nearest neighbor interactions described by -βH = K PN i=1 ~si · i~s +1. (a) Write down the transfer matrix hθ|T|θ′i, and show that it can be diagonalized with eigenvectors fm(θ) ∝ eimθ for integer m [Show More]

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