# Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

## TL;DR

This paper investigates the thermodynamic states of a mixed spin 1/2 and spin 1 hexagonal nanowire system using an improved mean field approximation, revealing detailed phase transition behavior including metastable states.

## Contribution

It introduces an improved mean field approach to analyze the thermodynamics of a mixed spin nanowire system, including metastable and unstable states, from a seven-site cluster.

## Key findings

- Identification of stable, metastable, and unstable states
- Calculation of Gibbs free energy, magnetization, and phase boundaries
- Discovery of phase transitions in metastable branches

## Abstract

The mean field approximation results in the mixed spin 1/2 Ising model and spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from the Bogoliubov inequality. The Gibbs free energy, magnetization and critical frontiers are obtained. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states.