Spin-wave bound-state energies from an Ising model

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Abstract
We study the two-dimensional classical Ising model that is equivalent, via the Suzuki-Trotter mapping, to the XXZ Heisenberg quantum-spin chain. By imposing appropriate boundary conditions to the Ising model, the spin waves of the quantum model are studied. We reproduce the entire energy spectrum of the two-spin-wave states and derive bound-state energies of the three-spin-wave states. Thus, the continuum energetics of the elementary excitations of a d-dimensional quantum model are contained in the equivalent (d+1)-dimensional classical model, even though the latter is a discrete-spin model.