BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional U(1) Ginzburg–Landau Model
Year: 2026
Type: article
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.
Source: Mathematics
DOI: 10.3390/math14203647
Authors: Hitomi Endo, Michikazu Kobayashi
Institution: Kochi University of Technology
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7206205166
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