A finite-size effect in the two-dimensional XY model is analytically obtained in the low-temperature limit. It is then shown that the sign of this effect may be changed by generalizing the boundary conditions to include twists over the system, and also that the finite-size effect may be entirely eliminated by adjusting the amplitude of these twists. At finite temperatures, up to ${\mathit{T}}_{\mathit{c}}$ , the finite-size effect is shown to be virtually eliminated through the application of a self-consistent condition for the twist amplitude. This self-consistent condition is given a simple motivation. The use of the dielectric function from Monte Carlo simulations on the two-dimensional Coulomb gas is also critically discussed.A finite-size effect in the two-dimensional XY model is analytically obtained in the low-temperature limit. It is then shown that the sign of this effect may be changed by generalizing the boundary conditions to include twists over the system, and also that the finite-size effect may be entirely eliminated by adjusting the amplitude of these twists. At finite temperatures, up to ${\mathit{T}}_{\mathit{c}}$, the finite-size effect is shown to be virtually eliminated through the application of a self-consistent condition for the twist amplitude. This self-consistent condition is given a simple motivation. The use of the dielectric function from Monte Carlo simulations on the two-dimensional Coulomb gas is also critically discussed.

Physical review. B, Condensed matterAug 1, 199551 citations

Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist

Gaurav Khairnar, Thomas Vojta

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.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.

arXiv:2312.04468Physical review. EFeb 12, 20255 citations

Numerical analysis of lattice models in low dimensions

Minoru Takahashi, 高橋實

Jan 1, 19950 citations

Monte Carlo simulation of quantum statistical lattice models

Hans A. De Raedt, Ad Lagendijk

Physics ReportsOct 1, 1985188 citations

Monte Carlo simulations of finite-size effects in Kosterlitz Thouless systems

F. Falo, L. M. Florı́a, R Navarro

The two-dimensional planar rotator and XY ferromagnetic models for finite lattice sizes (triangular network), with free and periodic boundary conditions, have been studied using Monte Carlo simulations. Thermodynamic quantities, suitable for comparison with experimental data, have been obtained. Heat capacity data are almost insensitive to the lattice size and to the type of boundary conditions, whereas susceptibility data are sensitive to both the lattice size and the boundary conditions. For the Kosterlitz-Thouless phase transition non-universal critical parameters are inferred. They depend on the lattice, the model and the boundary conditions. It is conjectured that the main differences between free and periodic boundary conditions are caused by the influence of the free surface on vortex energetics.The two-dimensional planar rotator and XY ferromagnetic models for finite lattice sizes (triangular network), with free and periodic boundary conditions, have been studied using Monte Carlo simulations. Thermodynamic quantities, suitable for comparison with experimental data, have been obtained. Heat capacity data are almost insensitive to the lattice size and to the type of boundary conditions, whereas susceptibility data are sensitive to both the lattice size and the boundary conditions. For the Kosterlitz-Thouless phase transition non-universal critical parameters are inferred. They depend on the lattice, the model and the boundary conditions. It is conjectured that the main differences between free and periodic boundary conditions are caused by the influence of the free surface on vortex energetics.

Journal of Physics Condensed MatterAug 7, 19896 citations

{\mathit{T}}_{\mathit{c}}

, the finite-size effect is shown to be virtually eliminated through the application of a self-consistent condition for the twist amplitude. This self-consistent condition is given a simple motivation. The use of the dielectric function from Monte Carlo simulations on the two-dimensional Coulomb gas is also critically discussed.