Structure factor of thin films near continuous phase transitions

TL;DR

This paper analyzes the two-point correlation function in thin films near critical points using renormalization group theory, predicting scattering behaviors and singularities relevant for X-ray and neutron experiments.

Contribution

It provides a theoretical framework for understanding correlation functions and scattering in thin films near phase transitions, incorporating surface effects and finite thickness.

Findings

Correlation function dependence on momentum, temperature, and film thickness

Calculation of grazing incidence scattering cross sections

Identification of singularities in correlation functions

Abstract

The two-point correlation function in thin films is studied near the critical point of the corresponding bulk system. Based on fieldtheoretic renormalization group theory the dependences of this correlation function on the lateral momentum, the two distances normal to the free surfaces, temperature, and film thickness are determined. The corresponding scattering cross section of X-rays and neutrons under grazing incidence is calculated. It reveals the various singularities of the two-point correlation function.