BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model
- 1School of Engineering Science, Kochi University of Technology, Kochi 782-8502, Japan
Abstract
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)∼r−2. The correlation and Binder ratios are nearly size-independent at low temperature and collapse with the BKT-type variable (T−TBKT)(logL)2; finite-size effects set in around T≃0.35–0.4, consistent with TBKT≃0.35. 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.
Versions
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BibTeX
@article{endo2026bktlike,
title = {{BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model}},
author = {Hitomi Endo and Michikazu Kobayashi},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203647},
url = {https://www.mdpi.com/2227-7390/14/20/3647},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model
AU - Hitomi Endo
AU - Michikazu Kobayashi
PY - 2026
DA - 2026/10/09
JO - Mathematics
DO - 10.3390/math14203647
UR - https://www.mdpi.com/2227-7390/14/20/3647
AB - 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)∼r−2. The correlation and Binder ratios are nearly size-independent at low temperature and collapse with the BKT-type variable (T−TBKT)(logL)2; finite-size effects set in around T≃0.35–0.4, consistent with TBKT≃0.35. 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.
SN - 2227-7390
ER -