Frustrated Spin System

img_lrg/three_spin.jpg not found

If the interaction energy between two spins is +1 if they point in the same direction, and -1 if they point in opposite directions, then this very simple spin system is frustrated. Spin 1 points up and spin 2 points down, so their interaction energy is -1. Spin 3 can point either up or down. If it points up, its interaction energy with spin 1 is +1 and its interaction with spin 2 is -1. If it points down, the opposite is true. So spin 3 is frustrated, and the simple rule for choosing a direction based on the lowest energy configuration does not help it pick a direction in which to point. (Unit: 9)