Recently I heard a report about the antiferromagnetic Ising model in triangular lattice. It's interesting and I never realized that the result in triangular lattice would be so different from square lattice. I'm curious about whether the following questions have been solved or what's the recent progress about the following question：
For homogeneous ferromagnetic Ising model in triangular lattice , I found the critical temperature can be exactly solved by Kramers-Wannier duality and star-triangle relation. $T_c= 3.642...K$, where $K$ is the coupling constant. But I haven't found the result of partion function. Has partition function of ferromagnetic Ising model in triangular lattice with and without external magnetic field been solved?
For homogeneous antiferromagnetic Ising model in triangular lattice, what's the ground state and ground state entropy? Does it exist phase transition? What's the partition function with or without external magnetic field?
I want to know whether these have been solved. If it's solved, please recommend some references.