Abstract
The properties of the antiferromagnetic Ising model in the critical magnetic field are investigated by evaluating exactly its all possible ground states on L × L square lattice (L = 4∼16) with free boundary conditions for the first time. From the exact integer values for the number of ground states Ωc(L) on L × L square lattice, the exact ground-state entropy (in unit of the Boltzmann constant kB) per volume sc(L) = L−2lnΩc(L) and the exact ground-state magnetization mc(L;T = 0) = L−2〈Σiσi〉 are calculated in the critical magnetic field, where σi is the magnetic spin on a lattice site i. The values of the ground-state entropy sc(L) and the ground-state magnetization mc(L), in the limit L → ∞, are accurately estimated to be sc/kB = 0.40750±0.00108 and mc = 0.54696±0.00065. In addition, for the first time, we estimate the values of the scaling exponents ωs and ωm, controlling the finite-size scaling behaviors of the ground-state entropy and the ground-state magnetization as sc−sc(L)∼L−ωs and mc−mc(L)∼L−ωm respectively. Our results show clearly that ωs = ωm = 1.
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