Exact density of states and Yang–Lee edge singularity of the triangular-lattice ising model in an external magnetic field

The Ising model in an external magnetic field on a triangular lattice is one of the most outstanding unsolved problems. The exact integer values for the density of states of the Ising model in an external magnetic field on a triangular lattice with L spins on a side are evaluated up to L=15 for the first time. Then, the exact distributions of the Yang–Lee zeros in the complex magnetic-field plane are obtained for the grand partition function of the Ising model in an external magnetic field on a triangular lattice, based on the exact density of states. The Yang–Lee edge singularity is one of the crucial properties of a magnetic spin system in an external magnetic field. For various physical systems, it has been extensively investigated in experimental and theoretical studies. Using the exact distributions of the Yang–Lee zeros, the Yang–Lee edge singularity of the Ising model in an external magnetic field on a triangular lattice is studied accurately for the first time.