Physics modeling

From SuperMe

Spin Glass Modelling

Project Members:

Research advisors: Dr. Susan McKay, Tom Stone, Mike Mihalco
REU student: Wen Luo

Abstract

As the computation power of computer grows rapidly, more and more physical material can be modeled theoretically with the computer. This leads us to a whole new field, since there are way too many restrictions on what a practical experiment can do. Our group is interested in study the materials that exhibit spin glass. Spin glass exhibits disordering and high magnetic frustration. Frustration causes the system to have a rough free energy landscape. So, a part of my project is to observe the change of the energy level for the system by letting the system cool down to a local energy minimal state, and heat it up so that it will report another local minimal state. The process is going to be repeated multiple times. Then I will analysis the local minimal states that I get and find out if there is a relationship between the states. Another part of my project is to improve the code we have right now, which takes weeks to run on a PC. We want to parallelize the code so that we will be able to use the supercomputer to be able to run a much larger data base.

Background

1. Ising Model

The Ising Model is a model of a magnet. Since the magnetism of a bulk material is made up of the combined magnetic dipole moments of many atomic spins within the material, the Ising Model stimulate such magnetism by postulate a lattices with magnetic dipole or spin on each site. Each site carries a value of 1 or -1 which represents up-spin or down-spin. Let s_i and s_j represents the spins on any two neighbor site, let J donates the bond energy between the two sites. The energy of the system can is defined to be:

2. Monte Carlo simulation

The basic idea behind Monte Carlo simulation is to flip a randomly chosen spin within the system, and check the energy level of the new state. If the energy level goes down, we accept the flip and do another Monte Carlo step on the new state; if the energy level goes up, there is a probability of it being accepted based on the temperature of the system, or otherwise we refuse this change of state and redo the Monte Carlo step on the original state. This process will be repeated for a large amount of time so that the system will reach the ground state.

Schedule

Week 1 (05/26-06/01): SuperMe program orientation
Week 2 (06/02-06/08): Reading books on Monte Carlo simulation, Spin Glass, and Networking. Review existed journal on our topic
- Week 2 Report
Week 3 (06/09-06/15): Study the simulation code that we have already, try to speed up the code
- Week 3 Report
Week 4 (06/16-06/22): Modify the code so that we will be able to run it on the supercomputer
- Week 4 Report
Week 5 (06/23-06/29): Continue working on the code and start stimulation
- Week 5 Report
Week 6 (06/30-07/06): Continue stimulation with different initial state
- Week 6 Report
Week 7 (07/07-07/13): Record and analysis the data
- Week 7 Report
Week 8 (07/14-07/20): Finishing up the experiments and draw a conclusion
Week 9 (07/21-07/27): Working on the research report
- Report due on Thursday, July 24
Week 10 (07/28-08/01): working on the poster and presentation
- Poster due Thursday, July 31
- Final Symposium on Friday August 1

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