Dependence of ground state energy of classical n-vector spins on n

Samarth Chandra

doi:10.1103/physreve.77.021125

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arXiv · 0707.0688

Dependence of ground state energy of classical n-vector spins on n

Samarth Chandra

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Abstract

We study the ground state energy E_G(n) of N classical n-vector spins with the hamiltonian H = - \sum_{i>j} J_ij S_i.S_j where S_i and S_j are n-vectors and the coupling constants J_ij are arbitrary. We prove that E_G(n) is independent of n for all n > n_{max}(N) = floor((sqrt(8N+1)-1) / 2) . We show that this bound is the best possible. We also derive an upper bound for E_G(m) in terms of E_G(n), for m j} |J_ij| + E_G(n)) / (\sum_{i>j} |J_ij|). We describe a procedure for constructing a set of J_ij's such that an arbitrary given state, {S_i}, is the ground state.

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Samarth Chandra. 2007-07-04. Dependence of ground state energy of classical n-vector spins on n. https://doi.org/10.1103/physreve.77.021125

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