Hübscher David M, Wessel Stefan
JARA-HPC High Performance Computing, JARA-FIT Fundamentals of Future Information Technology, Institute for Theoretical Solid State Physics, RWTH Aachen University, D-52056 Aachen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):062112. doi: 10.1103/PhysRevE.87.062112. Epub 2013 Jun 10.
We study the thermal phase transitions in the generalized classical XY model on the two-dimensional square lattice using single-cluster Monte Carlo simulations. In particular, we examine the (spin-wave) stiffness (helicity modulus) jump at the transition between the low-temperature algebraic phases and the disordered high-temperature regime. Employing a finite-size scaling ansatz from conformal field theory to estimate the termination of the algebraic phases that does not require knowledge of the critical properties, we provide an unbiased estimate of the stiffness jump. Our results are in full accord with the Berzinskii-Kosterlitz-Thouless scenario, i.e., the jump in the helicity modulus does not depend explicitly on the strength of the nematic coupling, but relates directly to the vorticity of the vortex excitations that drive the phase transition. We comment on previous work on related models, where Berzinskii-Kosterlitz-Thouless transition temperatures were based on scaling assumptions contradicted by our findings.
我们使用单团簇蒙特卡罗模拟研究二维正方晶格上广义经典XY模型中的热相变。特别地，我们考察了低温代数相和无序高温区之间转变处的（自旋波）刚度（螺旋度模量）跃变。通过采用共形场论中的有限尺寸标度假设来估计代数相的终止，这不需要临界性质的知识，我们给出了刚度跃变的无偏估计。我们的结果与贝津斯基-科斯特利茨- Thouless 图景完全一致，即螺旋度模量的跃变并不明确依赖于向列耦合的强度，而是直接与驱动相变的涡旋激发的涡度相关。我们对先前关于相关模型的工作进行了评论，在那些工作中，贝津斯基-科斯特利茨- Thouless 转变温度是基于与我们的发现相矛盾的标度假设。
