# First-Order Phase Transition

## INTRODUCTION

Phase transitions involve a sudden change in the physical properties of a system as temperature, pressure, or other thermodynamic variable changes. The most familiar example is the boiling of water, or, equivalently, the condensation of steam. In this case, density is the physical property that changes abruptly on passing through the boiling point.

## THE PROJECT

In this project we'll study a seemingly different, but, in fact, closely related phase transition: the spontaneous magnetization of a ferro-magnetic material. Our "material" is a two-dimensional lattice of "spins," in which each spin can take on values from -1.0 to +1.0.

The simulation involves generating random configurations of spins, subject to the constraint that they obey the Boltzmann distribution at a given temperature. You'll use the Metropolis Monte-Carlo algorithm for this. You'll start at a high temperature, and gradually cool the system down to absolute zero. During the course of the simulation you'll gather statistics such as the average magnetization of the system, and its variance. At high temperatures you should find the average magnetization to be nearly zero. As the temperature passes through the Curie point (the magnetic equivalent of the boiling point) the average magnetization will tend towards +1.0 or -1.0. The variance should reach a maximum at the Curie point.

The end result of the simulation is to produce a video that is qualitatively like the example one, and to determine the Curie point for this system.

Dave Ennis is the OSC coordinator for the Phase Transition project. Dave's office is in 420-4. Please contact Dave to set up appointment(s) for consultation.

For assistance, write si-contact@osc.edu or call 614-292-0890.