# Phase transitions from ising model

1. Nov 18, 2007

### coolnessitself

I'm having trouble understanding how changing parameters in the ising model leads to first order phase transitions. I understand how the intersection of
$\frac{kT}{2nJS} (\eta - \frac{g \mu_o H_o}{kT} ) = B_s(\eta)$
where $B_s(\eta)$ is the Brouillion func leads (in the absence of a field H) to one stable state for high T and low T, and how if T is in between this there are three solutions, leading to symmetry breaking. What I don't get is what happens with a magnetic field. Say T is chosen such that we've got three solutions still. The linear component will shift, so one solution will be more stable than the other, but how can you tell which one?