Project SEED 2009

Project SEED 2009

supported by American Chemical Society

Topic

Studying materials with computers

Goal

To understand magnetic phase transition using 2-dimensional Ising model and Monte Carlo simulations

Participants

Shenelle Alleyne (Irvington High School, Irvington, NJ)

Mayrolin Garcia (Irvington High School, Irvington, NJ)

Alibek Medetbekov (Science Park High School, Newark, NJ)

Advisors

Prof. Ken Ahn (NJIT)

Tsezar Seman (NJIT)

Project SEED Program Advisor

Ms. Susan Fahrenholtz

Pictures

Picture1, Picture2

Hours

Monday-Thursday: 9am-4pm in Computer Lab at Tiernan Hall, NJIT

Friday: Work on assignment at home

Syllabus

Week 1: 7/1/09 – 7/3/09: Introduction

Literature search on ferromagnetism, electron spin, Ising model, phase transition, ferromagnetic phase transition, Curie temperature

Week 2: 7/6/09 – 7/10/09: Learning about C++

Take C++ lectures by Seman and practice programming (Outline for Lectures on C++)

Literature search on absolute temperature, energy, exchange energy, Boltzmann constant

Week 3: 7/13/09 – 7/17/09: Random number for math problem

Generate random number between 0 and 1

Find the area of a circle using random numbers

Week 4: 7/20/09 – 7/24/09: Random number for 1D chain

Write a code which calculates the energy of a 1D Ising model

Find the ground state of the 1D Ising model using random numbers

Week 5: 7/27/09 – 7/31/09: Random number for 2D lattice

Write a code which calculates the energy of a 2D Ising model

Find the ground state of the 2D Ising model using random numbers

Week 6: 8/3/09 – 8/7/09 : Introduce temperature

Write a code which includes the Monte Carlo algorithm for finite temperatures

Plot energy versus simulation step and find the time range with the thermal equilibrium fluctuations

Week 7: 8/10/09 – 8/14/09: Find magnetic moment at a temperature

Plot magnetization versus simulation step and find the thermal average magnetic moment

Week 8: 8/17/09 – 8/21/09: Change temperatures and find phase transition

Change temperatures and plot magnetization versus temperature, and compare with experiments

Estimate the Curie temperature and compare with the exact value for 2D Ising model