Infrared bounds, phase transitions and continuous symmetry breaking
Infrared bounds, phase transitions and continuous symmetry breaking
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DOI：
10.1007/bf01608557
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发表时间：
1976-02
影响因子：
2.4
通讯作者：
J. Fröhlich;B. Simon;T. Spencer
中科院分区：
文献类型：
--
作者：
J. Fröhlich;B. Simon;T. Spencer
我们提出了一种新的方法，严格证明相变的存在。特别地，我们证明了在（φ·φ）32量子场论和3维或更多维的经典各向同性海森堡模型中相变的发生.证明的中心元素是，对于固定的铁磁最近邻耦合，两点函数inkspace的绝对连续部分以0（k−2）为界。在适用的情况下，我们的结果在数值上可以相当准确。例如，我们的下限的临界温度在三维伊辛（分别。经典Heisenberg）模型与高温膨胀得到的结果在14%以内（分别为9%）。
We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function inkspace is bounded by 0(k−2). When applicable, our results can be fairly accurate numerically. For example, our lower bounds on the critical temperature in the three dimensional Ising (resp. classical Heisenberg) model agrees with that obtained by high temperature expansions to within 14% (resp. a factor of 9%).