Lanczos exact diagonalization study of field-induced phase transitions for Ising and Heisenberg antiferromagnets

Using an exact diagonalization treatment of Ising and Heisenberg model Hamiltonians, we study field-induced phase transitions for two-dimensional antiferromagnets. It is found that a first-order phase transition occurs for both the Ising and Heisenberg antiferromagnets. For the Ising antiferromagnet a mixture of antiferromagnetic and ferromagnetic phases exists only at a critical value of Zeeman energy, while for the Heisenberg antiferromagnet the mixed phase appears over a wide range of Zeeman energy. It is shown that the mixed phase for the Heisenberg antiferromagnet occurs owing to the presence of a spin-flop process as an intermediate step.