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