Low-temperature impurity pairing in the frustrated 2D Ising model

We present exact results on the low-temperature behavior of the square lattice ±J Ising model, with a concentration c of ferromagnetic bonds and a concentration 1−c of antiferromagnetic bonds. We find that for T below a characteristic temperature T0, the system is “frozen” in the sense that its ground state properties coincide with measured quantities for systems of macroscopic size. We find that T0 is remarkably large, being roughly room temperature if J/kB ∼ 1000 K. We also study the effect on the free energy of various spatial arrangements of the ferromagnetic bonds.