Constraints on the two-particle distribution function due to the permutational symmetry of the higher order distribution functions

TL;DR

This paper derives constraints on the two-particle distribution function imposed by the permutational symmetry of higher order distribution functions, providing bounds relevant for physical properties like magnetization.

Contribution

It introduces a method to determine restrictions on the two-particle distribution function based on symmetry requirements of higher order functions, including the infinite particle limit.

Findings

Derived bounds on two-particle distribution functions

Established limits on magnetization and susceptibility

Analyzed the case for two-value variables across all n

Abstract

We investigate how the range of parameters that specify the two-particle distribution function is restricted if we require that this function be obtained from the $n^{\rm th}$ order distribution functions that are symmetric with respect to the permutation of any two particles. We consider the simple case when each variable in the distribution functions can take only two values. Results for all $n$ values are given, including the limit of $n\to\infty$. We use our results to obtain bounds on the allowed values of magnetization and magnetic susceptibility in an $n$ particle Fermi fluid.