Comparison of the O ( 3 ) Bootstrap σ-Model with the Lattice Regularization at Low Energies
Comparison of the O ( 3 ) Bootstrap σ-Model with the Lattice Regularization at Low Energies
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O ( 3 ) Bootstrap σ 模型与低能格子正则化的比较
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. U.S
中科院分区：
文献类型：
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作者：
Hungary.;A. U.S
本文用连续形状因子Bootstrap方法计算了二维非线性O（3）σ模型中零外动量时由连通四点函数定义的重整化耦合gR，估计误差为0.3%。本文给出了格点正则化理论中gR的新的高精度数据，其标准作用量适用于近热力学格点L/L ~ 122，关联长度L ~ 122，不动点作用量适用于关联长度L ~ 122。形状因子和晶格结果之间的一致性在± 1%以内。我们还通过测量有限体积下的两粒子能量来重新计算低能下的相移，这是以前由Lüscher和Wolff使用标准作用量进行的任务，但这次使用固定点作用量。与Zamolodchikov S-矩阵的良好协议被发现。
The renormalized coupling g R defined through the connected 4-point function at zero external momentum in the non-linear O(3) sigma-model in two dimensions, is computed in the continuum form factor bootstrap approach with estimated error ∼ 0.3%. New high precision data are presented for g R in the lattice regularized theory with standard action for nearly thermodynamic lattices L/ξ ∼ 7 and correlation lengths ξ up to ∼ 122 and with the fixed point action for correlation lengths up to ∼ 12. The agreement between the form factor and lattice results is within ∼ 1%. We also recompute the phase shifts at low energy by measuring the two-particle energies at finite volume, a task which was previously performed by Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S-matrix is found.