具有弱吸引相互作用的粒子系统
Particle systems with weakly attractive interaction
摘要：
系统的经典连续粒子在巨正则系综相互作用，通过纯粹的吸引力，但稳定，相互作用的定义。通过晶格近似，FKG铁磁不等式被证明对这样的粒子系统成立。利用这些不等式，通过单调性和上界论证给出了无穷体积测度的一个构造。证明了无穷体积测度在欧氏变换下的不变性。该结构适用于任意的活动和温度和可积的长程相互作用。此外，可以处理具有不同“电荷”的粒子的非均匀系统。
英文摘要：
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such particle systems. Using these inequalities, a construction of the infinite volume measures is given by a monotonicity and upper bound argument. Invariance under Euclidean transformations is proven for the infinite volume measures. The construction works for arbitrary activity and temperature and for integrable long range interactions. Also, inhomogeneous systems of particles with different "charge" can be treated.
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