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

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

2007-07-04

arxiv.org/abs/0707.0688v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 figures, submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.77.021125

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 mj} |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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