Ising antiferromagnet in the critical magnetic field on square lattice with free boundary conditions
Seung‐Yeon Kim
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.
AIP conference proceedings•Jan 1, 2012•0 citations