Correlation length bounds for disordered Ising ferromagnets
Correlation length bounds for disordered Ising ferromagnets
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DOI：
10.1007/bf01225510
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发表时间：
1989-09
影响因子：
2.4
通讯作者：
J. Chayes;L. Chayes;D. Fisher;T. Spencer
中科院分区：
文献类型：
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作者：
J. Chayes;L. Chayes;D. Fisher;T. Spencer
研究了三维最近邻无序伊辛铁磁体：作为温度T和测量耦合波动大小的无序参数λ的函数。一个有限大小的尺度相关长度，ζf(T, λ)，是根据有限样本的磁响应定义的。在标度意义上，这个相关长度被证明是等价于淬灭平均相关长度ζ(T, λ)，定义为淬灭平均两点函数的渐近衰减率。进一步证明了定义ζ - fi的磁响应判据在临界点处具有标度不变的性质。以上结果可以证明，淬灭相关长度满足：，即淬灭相关长度指数的下限为≧2/d。
Thed-dimensional, nearest-neighbor disordered Ising ferromagnet:is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJij≧0. A finite-size scaling correlation length,ζf(T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζfis shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies:which implies the boundv≧2/dfor the quenched correlation length exponent.