de Queiroz S L, Stinchcombe R B
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro RJ, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036117. doi: 10.1103/PhysRevE.64.036117. Epub 2001 Aug 28.
Transfer-matrix methods are used to calculate spin-spin correlation functions (G), Helmholtz free energies (f) and magnetizations (m) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature T(c 0), on long strips of width L=3-18 sites, for binary field distributions. Analysis of the probability distributions of G for varying spin-spin distances R shows that describing the decay of their averaged values by effective correlation lengths is a valid procedure only for not very large R. Connections between field and correlation function distributions at high temperatures are established, yielding approximate analytical expressions for the latter, which are used for computation of the corresponding structure factor. It is shown that, for fixed R/L, the fractional widths of correlation-function distributions saturate asymptotically with L-2.2. Considering an added uniform applied field h, a connection between f(h), m(h), the Gibbs free energy g(m) and the distribution function for the uniform magnetization in a zero uniform field, P0(m), is derived and first illustrated for pure systems, and then applied for nonzero random field. From finite-size scaling and crossover arguments, coupled with numerical data, it is found that the width of P0(m) varies against (nonvanishing, but small) random-field intensity H0 as H(-3/7)(0).
转移矩阵方法用于计算二维随机场伊辛模型中，在接近零场体临界温度(T(c_0))时，宽度(L = 3 - 18)个格点的长条上，对于二元场分布的自旋 - 自旋关联函数（(G)）、亥姆霍兹自由能（(f)）和磁化强度（(m)）。对不同自旋 - 自旋距离(R)时(G)的概率分布分析表明，用有效关联长度描述其平均值的衰减仅对不太大的(R)是一个有效程序。建立了高温下场与关联函数分布之间的联系，得到了后者的近似解析表达式，用于计算相应的结构因子。结果表明，对于固定的(R/L)，关联函数分布的分数宽度以(L^{-2.2})渐近饱和。考虑施加一个均匀外场(h)，推导了(f(h))、(m(h))、吉布斯自由能(g(m))与零均匀场中均匀磁化强度的分布函数(P_0(m))之间的联系，首先在纯系统中进行了说明，然后应用于非零随机场。通过有限尺寸标度和交叉论证，结合数值数据，发现(P_0(m))的宽度随（非零但很小的）随机场强度(H_0)以(H_0^{(-3/7)})变化。
