Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long Range Interactions

TL;DR

This paper proves that in one-dimensional ferromagnetic O(N) spin models with long-range interactions, the two-point correlation function decays at a rate similar to the interaction itself for N=1,2,3,4 above the critical temperature.

Contribution

It establishes decay behavior of the two-point function in one-dimensional O(N) models with long-range interactions using Griffiths and Lieb-Simon inequalities.

Findings

Two-point function decays like the interaction for N=1,2,3,4

Decay holds for temperatures above T_c

Results apply to models with long-range interactions

Abstract

Using Griffiths and Lieb-Simon type inequalities, it is shown that the two-point function of ferromagnetic spin models with N components in one dimension decays like the interaction provided that N=1,2,3,4 and T > T_c.