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Updated: May 21, 2025

Magnetic Tweezers for the Measurement of Twist and Torque
Published on: May 19, 2014
Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist
Gaurav Khairnar1, Thomas Vojta1
1Missouri University of Science and Technology, Department of Physics, Rolla, Missouri 65401, USA.
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.
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