Problem 11P

Use a computer to produce a table and graph, like those in this section, for two interacting two-state paramagnets, each containing 100 elementary magnetic dipoles. Take a “unit” of energy to be the amount needed to flip a single dipole from the “up” state (parallel to the external field) to the “down” state (antiparallel). Suppose that the total number of units of energy, relative to the state with all dipoles pointing up, is 80; this energy can be shared in any way between the two paramagnets. What is the most probable macrostate, and what is its probability? What is the least probable macrostate, and what is its probability?

Solution

Step 1

we can model the two state paramagnet as an Einstein solid where the role of the oscillators is played by the dipoles, the energy quantum is the difference in energy between a parallel and antiparallel dipole. The antiparallel dipole has higher energy since a torque must be applied to twist the dipole against the field.