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摘要翻译：
本文研究了n个经典n向量自旋的基态能量E_G(n)，其哈密顿量为H=-\sum_{i>j}，J_ij，S_i，S_j，其中S_i和S_j是n向量，耦合常数J_ij是任意的。对于n>n_{max}(n)=flood((sqrt(8n+1)-1)/2),我们证明了E_G(n)与n无关。我们证明这个界是最好的。对于m<n,我们还用E_G(n)的形式导出了E_G(m)的一个上界。我们得到了一个由F(n)测量的受挫度的上界，定义为(\sum_{i>j}J_ij+E_G(n))/(\sum_{i>j}J_ij)。我们描述了构造一组J_ij的过程，使得任意给定的状态{S_i}是基态。
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英文标题：
《Dependence of ground state energy of classical n-vector spins on n》
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作者：
Samarth Chandra
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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<n. We obtain an upper bound on the frustration in the system, as measured by F(n), which is defined to be (\sum_{i>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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PDF链接：
https://arxiv.org/pdf/707.0688
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