Grüneberg Daniel, Hucht Alfred
Fakultät für Naturwissenschaften, Theoretische Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):036104. doi: 10.1103/PhysRevE.69.036104. Epub 2004 Mar 9.
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic whereby in the present work we focus on the isotropic case for which the model is found to be at its upper critical dimensionality. To investigate the critical behavior the temperature and field dependence of several quantities are studied by means of Monte Carlo simulations. On the basis of the Privman-Fisher hypothesis and results of the renormalization group the numerical data are analyzed in the framework of a finite-size scaling analysis and compared to finite-size scaling functions derived from a Ginzburg-Landau-Wilson model in zero mode (mean-field) approximation. The obtained excellent agreement suggests that at least in the present case the concept of universal finite-size scaling functions can be extended to the upper critical dimensionality.
我们研究了一种具有长程相互作用的二维伊辛模型，这种相互作用源自对具有面内自旋取向的自旋系统中磁偶极相互作用的推广。一般来说，这种相互作用是各向异性的，而在本工作中，我们关注的是各向同性情况，发现该模型处于其上限临界维度。为了研究临界行为，通过蒙特卡罗模拟研究了几个量对温度和场的依赖性。基于普里夫曼 - 费舍尔假设和重整化群的结果，在有限尺寸标度分析的框架内对数值数据进行了分析，并与从零模（平均场）近似下的金兹堡 - 朗道 - 威尔逊模型导出的有限尺寸标度函数进行了比较。所获得的极佳一致性表明，至少在当前情况下，通用有限尺寸标度函数的概念可以扩展到上限临界维度。
