一维分数U(1)金兹堡-朗道模型中的类BKT关联标度与扭转响应
BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional $U(1)$ Ginzburg--Landau Model
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中文总结 AI 辅助
研究一维分数U(1)金兹堡-朗道模型的类BKT关联标度与扭转响应，发现其关联行为类BKT但无普适螺旋度模量跃变。
中文摘要 AI 辅助
我们研究一维分数U(1)金兹堡-朗道模型，其二次项的傅里叶乘子为|k|^σ，重点关注临界情况σ=1。这种色散关系产生对数自旋波涨落，表明尽管是一维体系，仍存在类BKT行为。我们利用随机格罗斯-皮塔耶夫斯基动力学采样平衡吉布斯测度，并分析关联函数、无量纲比率、有效指数和扭转响应。关联函数在低温下呈现代数分支，其指数随温度变化；高温区域则表现出非局部核诱导的尾项，符合C(r)~r^(-2)的规律。低温下关联函数和宾德比率几乎与体系尺寸无关，且随BKT型变量(T-T_BKT)(log L)^2坍缩；有限尺寸效应在T≈0.35-0.4左右出现，与T_BKT≈0.35一致。与二维XY模型不同，扭转响应未产生有限螺旋度模量：普通线性响应量随体系尺寸增大，而尖点扭转响应按L^(-η(T))标度，与零模序参量的平方标度一致。因此，该相变在关联标度上是类BKT的，但缺乏普适的螺旋度模量跃变。
英文摘要
We study a one-dimensional fractional $U(1)$ Ginzburg--Landau model whose quadratic part has Fourier multiplier $|k|^σ$, focusing on the marginal case $σ=1$. This dispersion yields logarithmic spin-wave fluctuations, suggesting BKT-like behavior despite the one-dimensional setting. We sample the equilibrium Gibbs measure using stochastic Gross--Pitaevskii dynamics and analyze correlation functions, dimensionless ratios, effective exponents, and twist responses. The correlation function shows a low-temperature algebraic branch with a temperature-dependent exponent, while the high-temperature regime exhibits a nonlocal-kernel-induced tail consistent with $C(r)\sim r^{-2}$. The correlation and Binder ratios are nearly size independent at low temperature and collapse with the BKT-type variable $(T-T_{\rm BKT})(\log L)^2$; finite-size effects set in around $T\simeq0.35\text{--}0.4$, consistent with $T_{\rm BKT}\simeq0.35$. Unlike the two-dimensional XY model, twist responses do not yield a finite helicity modulus: the ordinary linear-response quantity grows with system size, whereas the cusp twist response scales as $L^{-η(T)}$, like the squared zero-mode order parameter. Thus, the transition is BKT-like in correlation scaling, but lacks a universal helicity-modulus jump.
发表机构
- School of Engineering Science, Kochi University of Technology（高知工科大学工程学部）
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