Allegheny Physics Professor Shafiqur Rahman, along with students Erin Brown, ’15, and Joshua Lawrence, ’15, have been conducting research in computer simulations in the area of statistical mechanics.

“My research, on a very fundamental level, is about short range interactions that can give rise to long range properties,” Rahman said.

These discovered properties can lead to a common consensus that helps to understand a larger system.

The computational strategies Rahman utilizes are widely applicable, making the example useful even if it is not specific. He compares his work to observing small groups of people interacting with each other in a way that can lead to a larger consensus about human interaction. The systems pertaining to physics that Rahman studies are enormously complicated.

“For example, a system of 100 items, each of which can have two possibilities, gives rise to astonishingly high number of possibilities, two to the 100. If a computer could generate a billion of these possibilities every second—a pretty tall order, it would take the computer longer than the age of the universe–about 15 billion years—to enumerate all the possibilities,” he said.

Therefore, scientists have to devise a computational method that will find patterns from a finite sample of usually 100,000 or a million of these possibilities. The properties calculated from the smaller sample can then lead to a more developed understanding of the larger system.

Subjects of the nature of the above example are defined as Ising Model problems, which deal with two possibilities at every site of the system. The problems Rahman researches have three or more possibilities, making the need for computational methods even more essential.

“[Monte-Carlo methods] found an early application in the development of the  first atomic bomb, but is now widely used in all areas of science, as well as humanities and social sciences,” Rahman said.

While he works with problems of fundamental nature, he often adapts his work to accommodate a student’s research interest. Lawrence, as someone who hopes to work on Wall Street, is interested in the application of Monte-Carlo Methods in finance, which they have been exploring over the past year.

“While most professors would stick to the specific application related to their research, Dr. Rahman is willing to learn new topics so that students may apply Monte-Carlo simulations to fields of their interest,” Lawrence said.

Lawrence has been accepted to Carnegie-Mellon University to pursue graduate work in the field of information systems management.

Brown, ’15, is a physics and math double major who began doing research with Rahman in her second year at Allegheny. She has benefitted greatly from her computational physics research with Rahman, which has led to new career opportunities and helped motivate her to pursue her doctorate in computational and mathematical engineering at Stanford University.

“Many problems in the modern sciences may benefit from computational approaches, and I think the skills that I have gained working with Dr. Rahman and that I will hone during my Ph.D. will equip me to tackle new and exciting computational problems throughout my career,” Brown said.

Throughout his career, Rahman has interacted with numerous student researchers and finds Brown and Lawrence particularly helpful. In addition to exploring Brown and Lawrence’s interests, the main research, in which alumnus Samuel Knarr, ’12 was involved,  has led to the development of a new way to predict phase transitions, a particular area of interest for those researching computational physics. Rahman has been researching the antiferromagnetic Potts Model. Antiferromagnetism relates to alternate electron spins that point in opposite directions.

Largely satisfied with their understanding of that area, they are moving on to researching systems that have defects, which will allow them to understand it further.