**
Project SEED**

** Funded 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**

Summer 2010

Jessica Lopez

Chad Michael Coviel

Rodolfo Ernesto Marquez

Erole Alexandre

Summer 2009

Shenelle Alleyne
(Irvington High School, Irvington, NJ)

Mayrolin Garcia (Irvington High School,
Irvington, NJ)

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

Summer 2007

Parth Patel

¡¡

**
Advisors**

Prof.
Ken Ahn (NJIT)

Tsezar Seman (NJIT)

**Project
SEED Program Advisor**

Ms. Susan Fahrenholtz

**
Hours**

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

Friday:
Work on assignment at home

**C/C++
related links**

**Free C/C++
compiler: **
Dev-C++

¡¡

**
Syllabus**

__Week
1: Introduction__

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

__Week
2: 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: Random number for math problem__

Generate
random number between 0 and 1

Find
the area of a circle using random numbers

__Week
4: 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: 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: 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: Find magnetic moment at a temperature__

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

__Week
8: 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

__Week
9: Summary__

Write
a report and prepare a poster

**
Examples of final reports
and codes**

Summer 2009

Shenelle Alleyne:
Report,
code

Alibek Medetbekov:
Report,
code