The classical and the quantum, spin S = 1 2 , versions of the uniaxially anisotropic Heisenberg antiferromagnet on a square lattice in a field parallel to the easy axis are studied using Monte Carlo techniques. For the classical version, attention is drawn to biconical structures and fluctuations at low temperatures in the transition region between the antiferromagnetic and spin-flop phases. For the quantum version, the previously proposed scenario of a first-order transition between the antiferromagnetic and spin-flop phases with a critical endpoint and a tricritical point is scrutinized.

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.

Square lattice Heisenberg and XY antiferromagnets with uniaxial anisotropy in a field along the easy axis are studied. Based on ground state considerations and Monte Carlo simulations, the role of biconical structures in the transition region between the antiferromagnetic and spin-flop phases is analyzed. In particular, adding a single-ion anisotropy to the XXZ antiferromagnet, one observes, depending on the sign of that anisotropy, either an intervening biconical phase or a direct transition of first order separating the two phases. 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. The exchange integral J is antiferromagnetic, J > 0, and the anisotropy parameter ∆ may vary from zero (Ising limit) to one (isotropic Heisenberg model). The magnetic field H acts along the easy axis, the z-axis. As known for many years 19 , the phase diagram of the XXZ model includes the long-range ordered antiferromagnetic (AF), the algebraically ordered spin-flop (SF), and the paramagnetic phases. Only very recently, attention has been drawn to the role of biconical (BC) structures and fluctuations, in the ground state and in the transition region between the AF and SF phases 6 . In a BC ground state configuration the spins on the two sublattices (i.e. on neighboring sites), A and B, form different cones around their two different tilt angles, θ A and θ B , with respect to the easy axis, see Fig. 1. In the XXZ model, these structures occur at the critical field, H c1 , which separates the AF and SF structures at T = 0. The two tilt angles of the BC ground states are interrelated by 6 . 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 re...

Classical uniaxially anisotropic Heisenberg and XY antiferromagnets in a field along the easy axis on a square lattice are analysed, applying ground state considerations and Monte Carlo techniques. The models are known to display antiferromagnetic and spin-flop phases. In the Heisenberg case, a singleion anisotropy is added to the XXZ antiferromagnet, enhancing or competing with the uniaxial exchange anisotropy. Its effect on the stability of non-collinear structures of biconical type is studied. In the case of the anisotropic XY antiferromagnet, the transition region between the antiferromagnetic and spin-flop phases is found to be dominated by degenerate bidirectional fluctuations. The phase diagram is observed to resemble closely that of the XXZ antiferromagnet without single-ion anisotropy.PACS. 68.35.Rh Phase transitions and critical phenomena -75.10.Hk Classical spin models -05.10.Ln Monte Carlo method, statistical theory

A two-dimensional Ising model with short-range interactions and mobile defects describing the formation and thermal destruction of defect stripes is studied. In particular, the effect of a local pinning of the defects at the sites of straight equidistant lines is analyzed using Monte Carlo simulations and the transfer matrix method. The pinning leads to a long-range ordered magnetic phase at low temperatures. The dependence of the phase transition temperature, at which the defect stripes are destabilized, on the pinning strength is determined. The transition seems to be of first order, with and without pinning.