2D Ising Model – Monte Carlo Simulation

Overview

This project implements a 2D Ising model simulation using the Metropolis Monte Carlo algorithm.

The system models a ferromagnetic lattice under thermal fluctuations and external magnetic field.

The simulation computes:

• Magnetization as a function of temperature
• Energy evolution
• Dependence on external magnetic field

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Physical Model

The Hamiltonian of the system is:

H = -J Σ s_i s_j - H Σ s_i

where:

• s_i = ±1 spin variable
• J = interaction strength
• H = external magnetic field

Periodic boundary conditions are applied.

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Numerical Method

• Random initial spin configuration
• Spin updates via Metropolis algorithm
• Thermal averaging over time steps
• Temperature sweep to analyze phase behavior

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Results

The simulation reproduces expected qualitative behavior:

• Decrease of magnetization with increasing temperature
• Dependence on external magnetic field
• Thermal fluctuations near critical region

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Requirements

• Python 3.x
• NumPy
• Matplotlib

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Author

Esther Menéndez BSc Physics