论文标题
一维iSing模型的敏感性：t = 0时的奇异性是必不可少的吗？
Susceptibility of the one-dimensional Ising model: is the singularity at T = 0 an essential one?
论文作者
论文摘要
一维iSing模型的零场等温敏感性与邻邻次相互作用和有限数量的旋转被证明具有相对简单的奇异性，而温度接近零，仅与逆温度成比例。这与无限链的整个文献中所看到的相反：一个基本奇异性，其中包括对反向温度的指数依赖性。假设有任意（但有限的）旋转和保留术语通常被认为是在热力学极限中可忽略的，则该分析涉及除直接串联膨胀以外的任何内容，这是从磁场中的封闭链的分区函数开始，使用传输矩阵方法获得；或从通过波动散动定理发现的零场敏感性的表达式中。在这两种情况下，指数的奇异性都完全消除了。另外，发现每旋转的易感性随旋转数量增加（除非非相互作用旋转），这一结果也与无限链条通常报道的相差。
The zero-field isothermal susceptibility of the one-dimensional Ising model with nearest-neighbor interactions and a finite number of spins is shown to have a relatively simple singularity as the temperature approaches zero, proportional only to the inverse temperature. This is in contrast to what is seen throughout the literature for the inifinite chain: an essential singularity that includes an exponential dependence on the inverse temperature. Assuming an arbitrary (but finite) number of spins and retaining terms that are usually considered ignorable in the thermodynamic limit, the analysis involves nothing beyond straightforward series expansions, starting either from the partition function for a closed chain in a magnetic field, obtained using the transfer-matrix approach; or from the expression for the zero-field susceptibility found via the fluctuation-dissipation theorem. In both cases, the exponential singularity is exactly removed. In addition, the susceptibility per spin is found to increase with the number of spins (except in the case of noninteracting spins), a result which is also at variance with what is normally reported for an infinite chain.
