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arXiv 1108.2425cond-mat.stat-mech
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表面临界现象的Monte Carlo研究:特殊点

A Monte Carlo study of surface critical phenomena: The special point

Martin Hasenbusch

摘要:

本文研究了半无限系统相图中的特殊点,这里的体跃迁属于三维伊辛普适类。为此,我们进行了有限尺寸标度研究的改进的Blume-Capel模型上的简单立方晶格与两种不同类型的表面相互作用。为了检验主要体修正的影响,我们还模拟了简单立方晶格上自旋为1/2的伊辛模型。我们准确地估计了这些模型中特殊点处的表面增强耦合。我们找到了特殊跃迁的表面重整化群指数的$y_{t_s}=0.718(2)$和$y_{h_s}=1.6465(6)$。这些结果与以前用场论方法和自旋为1/2的伊辛模型的蒙特卡罗模拟得到的结果进行了比较。此外,我们还研究了特殊点附近的表面转变行为,最后讨论了在一个表面上具有特殊边界条件而在另一个表面上具有固定边界条件的薄膜。

英文摘要:

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interactions. In order to check for the effect of leading bulk corrections we have also simulated the spin-1/2 Ising model on the simple cubic lattice. We have accurately estimated the surface enhancement coupling at the special point of these models. We find $y_{t_s}=0.718(2)$ and $y_{h_s}=1.6465(6)$ for the surface renormalization group exponents of the special transitions. These results are compared with previous ones obtained by using field theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we study the behaviour of the surface transition near the special point and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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