Creutz Demon — 2D Ising Model Simulation

C++ implementation of the Creutz demon algorithm applied to the 2D Ising spin lattice.
The project studies the thermodynamic behavior of a 2D Ising system using a microcanonical Monte Carlo simulation and analyzes energy histograms, magnetization, and temperature dependence.

📄 Note: The full report (sprawozdanie) is written in Polish and available in the file Sprawozdanie.pdf.

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🧠 Project Overview

This project implements the Creutz demon algorithm for the two-dimensional Ising model.
It allows simulation of spin interactions on a lattice and analysis of phase transition behavior near the critical temperature.

The algorithm introduces an auxiliary variable — the demon — that exchanges energy with the system while keeping total energy constant, enabling a microcanonical ensemble simulation.

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⚙️ Implementation Details

• Language: C++17
• Environment: CLion 2024.3.4 (JetBrains)
• Compiler: GCC
• Key libraries: <vector>, <map>, <random>, <cmath>, <fstream>, <iostream>, <filesystem>

The program reads input parameters from stdin or a file and generates:

• histogram/ – energy distribution of the demon (E_demon, N(E), ln(N))
• magnetization/ – time evolution of magnetization during Monte Carlo sweeps
• mT.txt – summary file containing demon energy, temperature, average magnetization ⟨m⟩, and slope of the energy distribution

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🧩 Input Parameters

Example input format: Lx Ly numSweeps numEnergies E_demon_1 E_demon_2 ... E_demon_N

37 37 10000 10 56 128 256 512 768 960 1112 1280 1400 1520

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📊 Output Data

After the simulation, the program generates:

File	Description
mT.txt	Table of results: demon energy, temperature, ⟨m⟩, slope
histogram/histogram_E=...txt	Histogram of demon energy
magnetization/magnetization_E=...txt	Magnetization as a function of Monte Carlo steps

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🧪 Results Summary

• The simulation reproduces the expected phase transition in the 2D Ising model.
• The computed critical temperature was T_c^(sim) ≈ 2.3237 J/kB
• The magnetization ⟨m⟩ decreases sharply near the critical point, showing a clear transition from the ferromagnetic to the paramagnetic phase.

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🧾 Report (in Polish)

The complete analysis, theoretical background, methodology, and discussion of results are presented in the Polish-language report:

📘 DemonCreutz.pdf

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📂 Repository Structure

CreutzIsing2D/ ├── main.cpp # Source code
├── Sprawozdanie.pdf # Full Polish report
├── mT.txt # Summary results file
├── histogram/ # Energy distribution data
├── magnetization/ # Magnetization over MC sweeps
├── report_latex/ # LaTeX source files
│ ├── main.tex
│ ├── bibliography.bib
│ ├── histogramLin.png
│ ├── HistogramLog.png
│ ├── magnetization1000.png
│ ├── magnetyzacjaALL.png
│ └── mT.png
└── README.md

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📚 LaTeX Source

The full Polish report was written in LaTeX and is available in the /report_latex directory.

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🧑‍💻 Author

Created for educational purposes by Avui.