Correlation functions by Cluster Variation Method for Ising model with NN, NNN and Plaquette interactions

TL;DR

This paper applies the Cluster Variation Method to compute correlation functions in the Ising model with complex interactions, analyzing phase diagrams and disorder lines in 2D and 3D, with implications for experimental systems.

Contribution

It extends the CVM to calculate correlation functions and phase diagrams for Ising models with multiple interactions, including comparison with known models.

Findings

Calculated phase diagrams and disorder lines in 2D and 3D Ising models.

Identified regions with exponential and oscillating correlation behaviors.

Compared results with the eight-vertex model for validation.

Abstract

We consider the procedure for calculating the pair correlation function in the context of the Cluster Variation Methods. As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to the nearest neighbors and plaquette interactions in two and three dimensions. In presence of competing interactions, the so called disorder line separates in the paramagnetic phase a region where the correlation function has the usual exponential behavior from a region where the correlation has an oscillating exponentially damped behavior. In two dimensions, using the plaquette as the maximal cluster of the CVM approximation, we calculate the phase diagram and the disorder line for a case where a comparison is possible with results known in literature for the eight-vertex model. In three dimensions, in the CVM cube approximation, we calculate the phase diagram and the disorder line in some cases of particular interest. The relevance of our results for experimental systems like mixtures of oil, water and surfactant is also discussed.