We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness $ρ_s$ and the dimensionless wrapping probability $R$. From the finite-size scaling analyses of $ρ_s$ and of $R$, we determine the critical points as $T_c ({\rm XY}) =2.201\, 844 \,1(5)$ and $T_c ({\rm Villain})=0.333\, 067\, 04(7)$ and $(t/U)_c ({\rm BH})=0.059 \, 729 \,1(8)$, where $T$ is the temperature for the classical models, and $t$ and $U$ are respectively the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to $T$ suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as $ν=0.671 \, 83(18)$. In addition, the critical exponent $η$ is estimated as $η=0.038 \, 53(48)$ by analyzing a susceptibility-like quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.
A Monte Carlo Study of the Dipolar Universality Class in Three Dimensions
Graduate School of Science, Osaka Metropolitan University（大阪公立大学理学研究科）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学中心（iTHEMS））；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institut des Hautes Études Scientifiques（高等科学研究所）
The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
我们研究了三维伊辛普适类中从普通曲面普适类到正规曲面普适类的交叉问题。这种交叉是相关的行为的二元混合物的膜附近的分层点和弱吸附在一个或两个表面。我们在简单立方晶格上对改进的Blume-Capel模型进行了蒙特卡罗模拟。我们考虑系统与膜的几何形状，在各种边界条件的应用。我们讨论了由表面引起的标度校正及其与所谓外推长度的关系。为此，我们分析的磁化曲线附近的薄膜表面的行为。对于普通曲面普适类，我们得到了重整化群指数y_{h_1} =0.7249（6）的精确估计.接下来，我们研究了热力学Casimir力在从普通到正常表面普适类的交叉区域。为此，我们计算的交叉有限尺寸标度函数的泰勒展开到二阶h_1周围h_1=0，其中h_1是在一个表面的外部场。我们检查泰勒展开的适用范围，通过模拟在有限的h_1值。最后研究了强吸附极限h_1 \rightarrow \infty的逼近。我们的结果证实了二维伊辛模型条纹的精确计算所得到的定性图象[D. B. Abraham和A. Maciolek，Phys. Rev. Lett. 105，055701（2010）]，3D伊辛模型的平均场计算和初步蒙特卡罗模拟，[T. F. Mohry等人，Phys.Rev.E81，061117（2010）]：对于h_1和膜厚度的某些选择，热力学卡西米尔力作为温度的函数改变符号，并且对于温度和h_1的某些选择，它也作为膜厚度的函数…
Exchange Monte Carlo for continuous-space Path Integral Monte Carlo simulation
The University of Tokyo（东京大学）；Institute for Physics of Intelligence, The University of Tokyo（东京大学物理智能研究所）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
