/2D_Ising_Simulation_CPP

Primary LanguageJupyter Notebook

2D Ising Simulation

This project simulates the 2D Ising model using Monte Carlo methods and calculates various thermodynamic properties such as energy, magnetization, specific heat, magnetic susceptibility, and Binder cumulant.

Table of Contents

Introduction

The Ising model is a mathematical model used in statistical mechanics to simulate the behavior of ferromagnetic materials. This simulation uses Monte Carlo methods to simulate the behavior of a 2D lattice of spins interacting with each other.

Installation

To run the simulation, you will need a C++ compiler that supports C++11 or later.

  1. Clone the repository:

    git clone https://github.com/MohiMozaffari/2D_Ising_Simulation_CPP.git

  2. Compile the code:

    g++ -o Ising_2D/main.cpp

Usage

To run the simulation, execute the compiled binary:

./main

The simulation will generate a CSV file containing the results of the simulation.

Simulation Parameters

  • Lattice Size (N): 16
  • Number of Ensembles (nens): 25
  • Number of Ensembles in Critical Region (nens_crit): 50
  • Minimum Temperature (tmin): 2
  • Maximum Temperature (tmax): 3.0
  • Upper Critical Temperature (tcrit_up): 2.3
  • Lower Critical Temperature (tcrit_down): 2.2
  • Temperature Step Size (deltat): 0.2
  • Temperature Step Size Near Critical Region (deltat_crit): 0.01
  • Number of Monte Carlo Steps per Temperature (steps): N^3