Numerical studies of the two-dimensional XY model with symmetry-breaking fields.
Numerical studies of the two-dimensional XY model with symmetry-breaking fields.
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具有对称破缺场的二维 XY 模型的数值研究。
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Ying
中科院分区：
文献类型：
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作者：
Ala;Granato;Kankaala;Kosterlitz;Ying
本文给出了具有四重和八重对称性破缺场的二维XY模型的数值研究结果。这个模型最近被证明可以描述氢在W（100）表面引起的重构。基于平均场和重整化群参数，我们首先展示了各向异性场之间的相互作用如何在模型中引起不同的相变。当电场相互兼容时，当四阶电场由负值变为正值时，存在连续的相变。这种转变在低温时变得不连续。这两种制度是由一个多重临界点分开的。在四重场和八重场竞争的情况下，低温下的一阶跃迁打开为两个伊辛跃迁。然后，我们使用数值方法来精确定位多临界点的位置，并验证过渡的性质。所使用的不同技术包括结合有限尺寸缩放分析的蒙特卡罗直方图方法、实空间蒙特卡罗重整化群方法和蒙特卡罗传递矩阵方法。我们的数值计算结果与理论论点很好地吻合。
We present results of numerical studies of the two dimensional XY model with four and eight fold symmetry breaking fields. This model has recently been shown to describe hydrogen induced reconstruction on the W(100) surface. Based on mean-field and renormalization group arguments,we first show how the interplay between the anisotropy fields can give rise to different phase transitions in the model. When the fields are compatible with each other there is a continuous phase transition when the fourth order field is varied from negative to positive values. This transition becomes discontinuous at low temperatures. These two regimes are separated by a multicritical point. In the case of competing four and eight fold fields, the first order transition at low temperatures opens up into two Ising transitions. We then use numerical methods to accurately locate the position of the multicritical point, and to verify the nature of the transitions. The different techniques used include Monte Carlo histogram methods combined with finite size scaling analysis, the real space Monte Carlo Renormalization Group method, and the Monte Carlo Transfer Matrix method. Our numerical results are in good agreement with the theoretical arguments.