### Hysteresis

Introduction

Hysteresis is a nonequilibrium phenomenon and is a manifestation of a system that remains in a local minimum for some time before it switches to the global minimum. For example, when a ferromagnetic system such as the Ising model is magnetized in one direction by an external magnetic field H, its magnetization will not change immediately when H is changed.

Problems

1. Choose T = 1.8, the initial magnetic field H = 1, ΔH = 0.01, and 10 mcs for each value of H. The program plots the mean magnetization m for each value of H, and changes H by ΔH until H reaches H = -1, when it changes ΔH to -ΔH. Describe what you obtain and why it occurred. The resulting curve is called a hysteresis loop, and is characteristic of discontinuous (first-order) phase transitions.
2. In the simulation of Problem 1, what value of the field is needed to reduce the magnetization to zero? This value of H is called the "coercive field." The value of m when H = 0 is called the "remnant" magnetization.
3. Repeat Problem 1, but with T = 3. Do you observe any differences in the m versus H plot?
4. Change the number of mcs per field value to 1 and view the resulting plot for m versus H. Repeat for mcs per field value equal to 100. Explain the differences you see.

Java Classes Used

• Ising2DHysteresisApp
• Ising2D

Updated 3 March 2009.