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تسجيل مستخدم جديدThe phase-diagram of the Blume-Capel-Haldane-Ising spin chain
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We consider the one-dimensional spin chain for arbitrary spin $s$ on a periodic chain with $N$ sites, the generalization of the chain that was studied by Blume and Capel cite{bc}: $$H=sum_{i=1}^N left(a (S^z_i)^2+ b S^z_iS^z_{i+1}right).$$ The Hamiltonian only involves the $z$ component of the spin thus it is essentially an Ising cite{Ising} model. The Hamiltonian also figures exactly as the anisotropic term in the famous model studied by Haldane cite{haldane} of the large spin Heisenberg spin chain cite{bethe}. Therefore we call the model the Blume-Capel-Haldane-Ising model. Although the Hamiltonian is trivially diagonal, it is actually not always obvious which eigenstate is the ground state. In this paper we establish which state is the ground state for all regions of the parameter space and thus determine the phase diagram of the model. We observe the existence of solitons-like excitations and we show that the size of the solitons depends only on the ratio $a/b$ and not on the number of sites $N$. Therefore the size of the soliton is an intrinsic property of the soliton not determined by boundary conditions.
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