## Frustration

If the interaction energy $J$ in the Ising model is negative, then neighboring spins
lower their energy by being antiparallel. Such a system is called an *antiferromagnet*. The 2d Ising antiferromagnet
on a triangular or hexagonal lattice has some unusual properties. Each site has six nearest neighbors, and
it is impossible to create a microstate where every spin has only antiparallel neighboring spins.
We say the spin is *frustrated*. The goal of this simulation is to explore the effect of frustration on the possibility for a phase transition.

**Problem: Ising Antiferromagnetic on a hexagonal lattice**

Consider the Ising antiferromagnetic on a hexagonal lattice, for which each spin has six nearest
neighbors. The ground state in this case is not unique because of
*frustration* Convince yourself
that there are multiple ground states. Is the entropy zero or
nonzero at $T=0$? ($S(T=0) = 0.3383kN$. See G. H. Wannier, “Antiferromagnetism. The triangular Ising net,”
Phys. Rev. **79**, 357-364 (1950); erratum, Phys. Rev. B **7**, 5017 (1973).) Use Program `Frustration` to simulate
the antiferromagnetic Ising model on a hexagonal lattice at various temperatures and describe its
qualitative behavior. This system does not have a phase transition for $T>0$.
Are your results consistent with this behavior?

## Resource

Problem 5.41 in*Statistical and Thermal Physics: With Computer Applications*, 2nd ed., Harvey Gould and Jan Tobochnik, Princeton University Press (2021).