Diffuse scattering on Ising chain with competing interactions

TL;DR

This paper derives an exact analytical expression for the Fourier-transform of the pair spin-spin correlation function in a 1D Ising chain with competing interactions, analyzing how scattering evolves with temperature and interaction parameters.

Contribution

It provides a rigorous analytical solution for the Fourier-transform of the correlation function in a 1D Ising model with both nearest and next-nearest neighbor interactions.

Findings

Analytical expression for Fourier-transform of correlation function obtained.

Temperature-dependent scattering behavior analyzed.

Effects of exchange parameter variations on scattering studied.

Abstract

We considered the Ising 1D chain in an external magnetic field taking into account the nearest and next-nearest neighbor interactions. By the method of Kramers--Wannier transfer-matrix, the rigorous analytical expression for Fourier-transform of pair spin-spin correlation function was obtained, and the temperature evolution of the scattering was analyzed for various relations of exchange parameters.