Abstract
We study the response of a two-dimensional classical XY model to a finite (noninfinitesimal) twist of the boundary conditions. We use Monte Carlo simulations to evaluate the free energy difference between periodic and twisted-periodic boundary conditions and find deviations from the expected quadratic dependence on the twist angle. Consequently, the helicity modulus (spin stiffness) shows a nontrivial dependence on the twist angle. We show that the deviation from the expected behavior arises because of the mixing of states with opposite chirality which leads to an additional entropy contribution in the quasi-long-range ordered phase. We give an improved prescription for the numerical evaluation of the helicity modulus for a finite twist, and we discuss the spontaneous breaking of the chiral symmetry for the antiperiodic boundary conditions. We also discuss applications to discrete spin systems and some experimental scenarios where boundary conditions with finite twist are necessary.
Recommended Citation
G. Khairnar and T. Vojta, "Helicity Modulus and Chiral Symmetry Breaking for Boundary Conditions with Finite Twist," Physical Review E, vol. 111, no. 2, article no. 024114, American Physical Society, Feb 2025.
The definitive version is available at https://doi.org/10.1103/PhysRevE.111.024114
Department(s)
Physics
International Standard Serial Number (ISSN)
2470-0053; 2470-0045
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2025 American Physical Society, All rights reserved.
Publication Date
01 Feb 2025
Comments
National Science Foundation, Grant DMR-1506152