二维O(4)模型的尖锐质量界
Sharp mass bounds for the two-dimensional O(4) model
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具体内容
该稿件研究二维最近邻O(4)模型。作者声称对充分大的逆耦合β，完整转移间隙（含旋转不变局部可观测量扇区）被√β e^{−πβ}的正倍数上下夹住；并证明模型有唯一周期局部极限，且每个有限β>0处完整间隙为正，从而解决该周期态的全温度格点质量生成猜想。摘要还说明质量界在给定截断标度下对独立固定的物理单位一致，连续谱解释需额外收敛假设。手稿为AI产生，未经独立审查或同行评议。
- 声称大β时完整转移间隙由√β e^{−πβ}的正倍数上下界控制。
- 证明唯一周期局部极限及每个有限β>0处完整间隙为正。
- 作者称由此解决该周期态的全温度格点质量生成猜想。
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英文原始摘要
We prove sharp mass bounds for the two-dimensional nearest-neighbor $`O(4)`$ model. For all sufficiently large inverse couplings β, the full transfer gap, including rotation-invariant local-observable sectors, is bounded above and below by positive multiples of $`\sqrt\beta e^{-\pi\beta}`$. We also prove that the model has a unique periodic local limit and a positive full gap at every finite β > 0, resolving the all-temperature lattice mass-generation conjecture for this periodic state. Under the stated cutoff scaling, the mass bounds are uniform in independently fixed physical units. A continuum spectral interpretation requires separate convergence hypotheses for the transfer semigroup and the block observables.
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