Dependence of ground state energy of classical n-vector spins on n - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: We study the ground state energy E Gn of N classical n-vector spins withthe hamiltonian H = - \sum {i>j} J ij S i.S j where S i and S j are n-vectorsand the coupling constants J ij are arbitrary. We prove that E Gn isindependent of n for all n > n {max}N = floorsqrt8N+1-1 - 2 . We showthat this bound is the best possible. We also derive an upper bound for E Gmin terms of E Gn, for mj} |J ij| +E Gn - \sum {i>j} |J ij|. We describe a procedure for constructing a setof J ij-s such that an arbitrary given state, {S i}, is the ground state.



Author: Samarth Chandra

Source: https://arxiv.org/



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