Absence of Ordering in Certain Classical Systems

作者：N. David Mermin · 发表于：Journal of Mathematical Physics · 年份：1967 · DOI：10.1063/1.1705316 · 被引用次数：306 · 研究领域：Spectral Theory in Mathematical Physics、Quantum chaos and dynamical systems、Matrix Theory and Algorithms

A classical inequality giving lower bounds for fluctuations about ordered states is derived. The inequality, analogous to a quantum result due to Bogoliubov, is established by a purely classical argument which makes explicit the nature of the surface boundary conditions required, a point which is rather obscure in the quantum derivations. As in the quantum case the inequality is useful in excluding certain kinds of phase transitions in one- and two-dimensional systems. This is illustrated for several kinds of classical spin systems.