Square Ising ferromagnetic and antiferromagnetic lattices in a magnetic field: A new perturbation approach
Abstract
The incorporation of the magnetic interaction energy B into an effectiveexchange parameter in the transfer matrix has been used to probe the behavior of the square ferromagnetic and antiferromagnetic Ising lattices with nearestneighbor interactions ∊ in finite magnetic fields. The ferromagneticspecificheat capacity C (B,T) is proportional to ln(B∊) at the zerofield critical temperature T, when B∊<<1, in agreement with a previous analysis. The temperature T_{m} at which C (B,T) attains a maximum is initially depressed below T_{c}, while exhibiting a quadratic dependence on B. In larger fields, T_{m} turns around and is elevated, where now it is directly proportional to B. Qualitatively, this pattern exhibited by C (B,T) also is found with the meanfield approximation. The specificheat capacity for the antiferromagnetic lattice essentially retains its zerofield form through B∊<2 and exhibits a logarithmic divergence at the Neel temperature T_{N}(B), as does the magnetic susceptibility when B>0. The T_{N}(B) obtained through this method, over the range where the method is thought to be reliable, is in excellent agreement with previous work. Finally, some general features which are applicable to the threedimensional case are noted.
 Publication:

Physical Review B
 Pub Date:
 March 1978
 DOI:
 10.1103/PhysRevB.17.2305
 Bibcode:
 1978PhRvB..17.2305A
 Keywords:

 Antiferromagnetism;
 Crystal Lattices;
 Ferromagnetism;
 Magnetic Effects;
 Perturbation Theory;
 SpinLattice Relaxation;
 Critical Temperature;
 Free Energy;
 Magnetic Fields;
 Magnetic Permeability;
 Specific Heat;
 SolidState Physics