Spin-ordering in S = 1 anisotropic Heisenberg models with nondiagonal spin exchange

The properties of S = 1 anisotropic Heisenberg models with nondiagonal exchange between axial and planar spin components are investigated using Monte Carlo techniques. The quantum nature is taken into account in a semi-classical approximation. The ordering of the spins when applying an external field with axial and planar components is discussed. It is argued that the quantum nature of the spins and the nondiagonal exchange may explain the peculiar shape of the magnetic specific heat of FeBr2 as well as the weakly first-order phase transition observed in the same compound when a tilted field is applied.Comment: 9 pages, 15 figures included, to appear in European Physical Journal

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, 'weak' or 'strong', interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular $\beta_1 = 0.80 \pm 0.01$, are found to be robust against these perturbations.Comment: 7 pages, 13 figures, submitted to European Physical Journal

Dynamics of the two-dimensional directed Ising model: zero-temperature coarsening

We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from the directedness, or asymmetry, of the influence of the neighbours on the flipping spin. We show that the main characteristics of phase ordering at low temperature, such as self-similarity of the patterns formed by the growing domains, and the related scaling laws obeyed by the observables of interest, which hold for reversible dynamics, are still present when the dynamics is directed and irreversible, but with different scaling behaviour. In particular the growth of domains, instead of being diffusive as is the case when dynamics is reversible, becomes ballistic. Likewise, the autocorrelation function and the persistence probability (the probability that a given spin keeps its sign up to time $t$) have still power-law decays but with different exponents.Comment: 29 pages, 36 figure

Phase diagrams of Ising films with competing interactions

The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed.Comment: 7 pages, 6 figures included, version to appear in Eur. Phys. J.

Low temperature phase diagram and critical behaviour of the four-state chiral clock model

The low temperature behaviour of the four-state chiral clock ($CC_4$) model is reexamined using a systematic low temperature series expansion of the free energy. Previously obtained results for the low temperature phases are corrected and the low temperature phase diagram is derived. In addition, the phase transition from the modulated region to the high temperature paraphase is shown to belong to the universality class of the 3d-XY model.Comment: 17 pages in ioplppt style, 3 figure

Reply to a Comment

Reply to the Comment by F. Corberi, E. Lipiello and M. Zannetti (cond-mat/0211609)

Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here discuss rock-paper-scissors games on a one-dimensional lattice where the interaction rates and the mobility can be species dependent. Allowing only single site occupation, we realize mobility by exchanging individuals of different species. When the interaction and swapping rates are symmetric, a strongly enhanced swapping rate yields an increased mixing of the species, leading to a mean-field like coexistence even in one-dimensional systems. This coexistence is transient when the rates are asymmetric, and eventually only one species will survive. Interestingly, in our spatial games the dominating species can differ from the species that would dominate in the corresponding nonspatial model. We identify different regimes in the parameter space and construct the corresponding dynamical phase diagram.Comment: 6 pages, 5 figures, to appear in Physical Review

Ising cubes with enhanced surface couplings

Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor interactions and enhanced couplings between surface spins are studied. In particular, at the surface transition, the corner magnetization shows non-universal, coupling-dependent critical behavior in the thermodynamic limit. Results on the critical exponent of the corner magnetization are compared to previous findings on two-dimensional Ising models with three intersecting defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.

Ising films with surface defects

The influence of surface defects on the critical properties of magnetic films is studied for Ising models with nearest-neighbour ferromagnetic couplings. The defects include one or two adjacent lines of additional atoms and a step on the surface. For the calculations, both density-matrix renormalization group and Monte Carlo techniques are used. By changing the local couplings at the defects and the film thickness, non-universal features as well as interesting crossover phenomena in the magnetic exponents are observed.Comment: 8 pages, 12 figures included, submitted to European Physical Journal

Corrections to local scale invariance in the non-equilibrium dynamics of critical systems: numerical evidences

Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling properties of the response function of non-equilibrium critical systems in the aging regime following a quench from the high-temperature phase to the critical point. These predictions have been confirmed by Monte Carlo simulations and analytical results for some specific models, but they are in disagreement with field-theoretical predictions. By means of Monte Carlo simulations of the critical two- and three-dimensional Ising model with Glauber dynamics, we study the intermediate integrated response, finding deviations from the corresponding LSI predictions that are in qualitative agreement with the field-theoretical computations. This result casts some doubts on the general applicability of LSI to critical dynamics.Comment: 4 pages, 2 figures, minor changes, version to appear in Phys. Rev. B as a Rapid Communicatio