相互作用するBose-Einstein凝縮体の繰り込み群研究 II 有限温度でのd≦4に対する異常次元η

Takuma Ishikawa, Takehiko Oguchi

The phase transition for the spin systems described by the Hamiltonian H =-2 J ∑ < i , j > (ξ S i x S j x +η S i y S j y + S i z S j z )- g µ H ∑ i S i z is studied by means of the high-temperature series expansion of the zero field susceptibility. The first five terms in the susceptibility series are explicitly obtained for the two-dimensional square lattice in the cases of (i) 0≤ξ≤1, η=0 and (ii) 0≤ξ=η≤1. The critical temperature T c and the critical exponent γ (susceptibility) are obtained as functions of the spin S and the anisotropy parameter ξ. The critical temperature has a finite value in the XY model (ξ=1, η=0) as well as the Heisenberg model (ξ=η=1). The simple formulae expressing T c and γ valid for arbitrary S and ξ are proposed.

Oegren Magnus, Karen V. Kheruntsyan

Yoshio Torii, Yoichi Suzuki, Mikio Kozuma +1 more

Jianping Zuo, Yuanxing Gui

The M operation is introduced in η - ξ spacetime to derive the tilde rules in thermo field dynamics (TFD). This leads to an explanation of the tilde system in TFD as the system in region II of η - ξ spacetime.

寿夫 鳥井, 陽一 鈴木, 幹男 上妻 +1 more

guobin ouyang

3.12 §4.2 在条件 ∂_η²φ_I ≪ (∂_ηφ_I)² 下把幅度-相位系统合并为线性薛定谔方程(命题 3.12.4.01)。本文对**合并后的最终方程**做精确 Madelung 分解(极分解 Ψ = R·e^{iφ}),回答一个 3.12 未显式处理的问题:**这个线性化究竟丢弃了什么?** 结论:(i) 3.12 的显式条件丢弃的是**相位曲率** ∂_η²φ(只出现在连续性方程);(ii) 相位方程中还存在独立的**幅度曲率**项 Q_M = −D·∂_η²|Ψ|/|Ψ|(几何量子势),其丢弃是隐含的第二个近似——**双重近似结构**(推论 3.13.3.02)。Q_M 在 σ* 邻域的量级恰为 ħ_geom:Q_M(0) = D = 10/7821 ≈ 0.001279,Q_M(η_b) = D·(390.05/391.05) ≈ 0.001275。把 Q_M 显式放回方程得到**曲率型非线性薛定谔方程** (3.13.12),非线性项 −D·∂_η²|Ψ|/|Ψ| 是幅度曲率型(微分非线性),区别于 Gross–Pitaevskii 的代数非线性 g|Ψ|²——这是几何框架自然涌现的闭包形式,也是 3.11 Higgs 呼吸模式缺失含时动力学的候选归宿(开放猜想,§6)。诚实边界:V(η) 无显式形式(3.12 §7.1 仅给 Ĥ_geom = −D∂_η² + V(η);10.67 §8.2 承认未构造),含 V 的式子均为形式恒等关系;本文不修改 3.12 原文,只指认其推导路径自身的近似特征。