Estimating the Curie temperature in MATLAB using Monte Carlo simulation methods: a detailed yet accessible guide

Part One: Introduction and Background

The Curie temperature is the temperature at which magnetic materials lose their magnetism. At this temperature point, an object no longer exhibits magnetism. Understanding the Curie temperature of a material is critical for many industrial applications, such as refrigeration and magnetic storage. Usually, we can measure the Curie temperature experimentally. However, computer simulations provide us with a bridge between theory and experiment, allowing us to estimate this important parameter without making actual measurements.

The Monte Carlo method is a statistical method that uses random samples to solve problems. It takes its name from the Monte Carlo Casino in Monaco because the method involves large amounts of random sampling. In the context of estimating the Curie temperature, we will use Monte Carlo methods to simulate the behavior of atoms or molecules in magnetic materials.

To keep this technical guide easy to understand, we'll avoid complex formulas. Instead, we'll uncover the core of this process through MATLAB code.

Start our MATLAB journey

First, make sure your MATLAB environment is ready and has the required toolboxes installed.

1. initialization

Before we begin, we first need to initialize some parameters.

% 参数初始化
num_atoms = 1000;     % 原子数量
max_iterations = 1e5;