Field-induced phase transitions in the bcc Ising antiferromagnet with nearest-neighbor interactions have been studied using a Monte Carlo method. The properties of $N\ifmmode\times\else\texttimes\fi{}N\ifmmode\times\else\texttimes\fi{}N$ lattices with periodic boundary conditions have been determined for $N\ensuremath{\le}16$ and the size effects analyzed using finite-size scaling theory. We find no field dependence of the critical exponents and only a slow variation of critical amplitudes in small fields in agreement with the "smoothness postulate." At low temperatures the critical-field curve shows a weak, but clear maximum which is about 2% greater than the zero-temperature value ${H}_{c}$ . Crossover to noncritical exponential behavior due to thermally induced spin flips is observed as we move away from the low-temperature phase boundary.Field-induced phase transitions in the bcc Ising antiferromagnet with nearest-neighbor interactions have been studied using a Monte Carlo method. The properties of $N\ifmmode\times\else\texttimes\fi{}N\ifmmode\times\else\texttimes\fi{}N$ lattices with periodic boundary conditions have been determined for $N\ensuremath{\le}16$ and the size effects analyzed using finite-size scaling theory. We find no field dependence of the critical exponents and only a slow variation of critical amplitudes in small fields in agreement with the "smoothness postulate." At low temperatures the critical-field curve shows a weak, but clear maximum which is about 2% greater than the zero-temperature value ${H}_{c}$. Crossover to noncritical exponential behavior due to thermally induced spin flips is observed as we move away from the low-temperature phase boundary.

Physical review. B, Solid stateNov 1, 197760 citations

Self-consistent field near the critical point in the Ising antiferromagnetic model

V. Ya. Krivnov, Oleg A. Olkhov, B. N. Provotorov +1 more

Theoretical and Mathematical PhysicsFeb 1, 19700 citations

Ground state degeneracy of the Ising antiferromagnets in the maximum critical field

Dragan Slavkov Hajdukovic, S. Milošević

The authors demonstrate that all Ising antiferromagnets with arbitrary many-neighboured interactions and in the maximum critical field, have highly degenerate ground states accompanied with non-zero residual entropies. The residual entropies vanish when the range of interaction tends to infinity. The proof is realised by an explicit calculation in the case of a one-dimensional many-neighboured Ising antiferromagnet, and by establishing bounds for the residual entropy in the case of an Ising system situated on a lattice with arbitrary number of dimensions. They also show that the established bounds may serve as estimates of frequently unknown actual values of the residual entropy.The authors demonstrate that all Ising antiferromagnets with arbitrary many-neighboured interactions and in the maximum critical field, have highly degenerate ground states accompanied with non-zero residual entropies. The residual entropies vanish when the range of interaction tends to infinity. The proof is realised by an explicit calculation in the case of a one-dimensional many-neighboured Ising antiferromagnet, and by establishing bounds for the residual entropy in the case of an Ising system situated on a lattice with arbitrary number of dimensions. They also show that the established bounds may serve as estimates of frequently unknown actual values of the residual entropy.

Journal of Physics A Mathematical and GeneralNov 1, 198216 citations

{H}_{c}

. Crossover to noncritical exponential behavior due to thermally induced spin flips is observed as we move away from the low-temperature phase boundary.