サイト間Coulomb相互作用が生み出す電荷自由度のBerezinskii‐Kosterlitz‐Thouless相の数値的検証

Yun-Da Hsieh, Ying-Jer Kao, Anders W. Sandvik

We test an improved finite-size scaling method for reliably extracting the critical temperature T BKT of a Berezinskii–Kosterlitz–Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness ρ s at T BKT in combination with the Kosterlitz–Nelson relation between the transition temperature and the stiffness, ρ s ( T BKT ) = 2 T BKT /π, we define a size-dependent transition temperature T BKT ( L 1 , L 2 ) based on a pair of system sizes L 1 , L 2 , e.g., L 2 = 2 L 1 . We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining T BKT ( L 1 , L 2 ). For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for L up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result T BKT = 0.8935(1) is several error bars above the previously best estimates of the transition temperature, T BKT ≈ 0.8929. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated T BKT because of the neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions.

Jean‐François Richard, Martin Robert-De-Saint-Vincent, Jay Man +4 more

Mark G. Friesen

The standard treatment of the Kosterlitz-Thouless-Berezinskii (KTB) transition is supplemented here by the inclusion of free-vortex screening effects. We obtain the high-density corrections to the KTB critical behavior. The size of the KTB critical region is extracted, and is found in most cases to be quite small. The tricritical point, separating second-order (KTB) phase transitions from first-order transitions, is also determined. We make predictions concerning similar KTB-like transitions, such as in the layered cuprate superconductors.

小林正人, 武次徹也

八木 徹, 長嶋 雲兵

Yukiyasu Ozeki, Keita Ogawa, Nobuyasu Ito

A simple and efficient numerical analysis is proposed for the Kosterlitz-Thouless (KT) phase transition. The nonequilibrium relaxation method is applied to it. The two-dimensional ferromagnetic XY models are investigated to show the efficiency. At the KT transition point as well as inside the KT phase, the nonequilibrium relaxation of magnetization from the all-aligned state shows an asymptotic power-law decay, m(t) approximately t(-lambda(T)). Only outside the KT phase, an asymptotic single exponential decay is observed. Using a standard scaling form m(t)=tau(-lambda)(-)m(t/tau) in this regime, where tau is the relaxation time at each temperature, we find a simple and efficient numerical estimation of the KT transition point and dynamical exponent. This method can be applied to various kinds of models which show the KT-like behavior.