Two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field

Abstract

The classical, square lattice, uniaxially anisotropic Heisenberg antiferromagnet in a magnetic field parallel to the easy axis is studied using Monte Carlo techniques. The model displays a longrange ordered antiferromagnetic, an algebraically ordered spin-flop, and a paramagnetic phase. The simulations indicate that a narrow disordered phase intervenes between the ordered phases down to quite low temperatures. Results are compared to previous, partially conflicting findings on related classical models as well as the quantum variant with spin S=1/2.

Biconical structures in two-dimensional anisotropic Heisenberg antiferromagnets

“…leading, in addition to the rotational symmetry in the xy-components of the spins in the BC and SF states, to a high degeneracy of the ground state. This degeneracy seems to give rise to a narrow intervening, possibly disordered phase in the (field H, temperature T )-phase diagram of the square lattice XXZ model, as discussed before 3,4,6 . In this communication, we study variants of the XXZ model, staying in two dimensions, by adding a single-ion anisotropy, and by reducing the XXZ to the anisotropic XY model.…”

“…In case of the anisotropic XY model, the degeneracy of the ground state, at a critical field, in antiferromagnetic, spin-flop, and bidirectional structures seems to result, as in the case of the XXZ model, in a narrow disordered phase between the antiferromagnetic and spin-flop phases, dominated by bidirectional fluctuations. Recently, two-dimensional uniaxially anisotropic Heisenberg antiferromagnets in a magnetic field along the easy axis have been studied theoretically rather intensively 1,2,3,4,5,6,7,8,9 , motivated by experiments on intriguing magnetic properties of layered cuprates 1,10,11,12,13 and by experimental findings on complex phase diagrams for other quasi twodimensional antiferromagnets 14,15,16,17,18 exhibiting, typically, multicritical behavior.A generic model describing such systems is the XXZ Heisenberg antiferromagnet on a square lattice, with the Hamiltonianwhere we consider the classical variant, with the spin at site i,, being a vector of length one. S i is coupled to its four neighboring spins S j at sites j.…”

“…A typical phase diagram is shown in Fig. 2, where we set ∆ = 0.8, as usual 3,4,19 , and D/J = 0.2. The phase boundaries are determined by finite-size extrapolations of the staggered susceptibilities, the specific heat, and the Binder cumulant 23 .…”

First-principles study of thermodynamical properties of random magnetic overlayers on fcc-Cu(001) substrate

“…This approach turned out to be quite useful in the past, though some limitations exist 15 . The shape of temperature dependence of the magnetization is influenced by the size L. It leads often to the situation that cumulants for different system sizes cross in one point corresponding to the Curie temperature 14 .…”

Anisotropic XY antiferromagnets in a field

“…Especially, mean-field approximation [2,4], Monte Carlo simulations [16,17,18,19,20,21,22,23], and renormalization group calculations [3,5,24,25,26] have been applied.…”