Low temperature expansion of the gonihedric Ising model
Low temperature expansion of the gonihedric Ising model
复制标题
角面体伊辛模型的低温膨胀
DOI：
10.1016/s0550-3213(98)00342-3
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
F. Wegner
中科院分区：
文献类型：
--
作者：
R. Pietig;F. Wegner
研究了d维立方格子上的（d - 1）维闭软自回避随机曲面模型。表面构型的能量由E = J（n2+ 4kn 4）给出，其中n2是边的数量，其中两个斑块以直角相交，n4是边的数量，其中4个斑块相交。该模型可以表示为一个具有铁磁最近邻、反铁磁次近邻和格斑相互作用的Z2自旋系统。它对应于Wegner和Savvidy介绍的一般自旋系统的一个特例。由于没有与表面积成比例的项，与普通伊辛模型相反，模型的裸表面张力消失。通过对Peierls论证的适当修改，我们证明了k = 0时存在无穷多个有序低温相.三维自由能的低温展开达到x38阶（x = e−βJ），表明当k > 0时，只有铁磁低温相保持稳定。分析的低温膨胀到x44阶的磁化强度，磁化率和比热在3维产生的临界指数，这是在协议与以前的结果。© 1998 Elsevier Science B.V.
We investigate a model of closed (d - 1)-dimensional soft-self-avoiding random surfaces on a d-dimensional cubic lattice. The energy of a surface configuration is given by E = J(n2+ 4kn4), where n2is the number of edges, where two plaquettes meet at a right angle and n4is the number of edges, where 4 plaquettes meet. This model can be represented as a Z2- spin system with ferromagnetic nearest-neighbour, antiferromagnetic next-nearest-neighbour- and plaquetteinteraction. It corresponds to a special case of a general class of spin systems introduced by Wegner and Savvidy. Since there is no term proportional to the surface area, the bare surface tension of the model vanishes, in contrast to the ordinary Ising model. By a suitable adaptation of Peierls' argument, we prove the existence of infinitely many ordered low temperature phases for the case k = 0. A low temperature expansion of the free energy in 3 dimensions up to order x38(x = e−βJ) shows that for k > 0 only the ferromagnetic low temperature phases remain stable. An analysis of low temperature expansions up to order x44for the magnetization, susceptibility and specific heat in 3 dimensions yields critical exponents, which are in agreement with previous results. © 1998 Elsevier Science B.V.