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Register a new userPhase diagram of the antiferromagnetic XY model in two dimensions in a magnetic field
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The phase diagram of the quasi-two-dimensional easy-plane antiferromagnetic model, with a magnetic field applied in the easy plane, is studied using the self-consistent harmonic approximation. We found a linear dependence of the transition temperature as a function of the field for large values of the field. Our results are in agreement with experimental data for the spin-1 honeycomb compound BaNi_2V_2O_3
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The existence of nonlinear objects of the vortex type in two-dimensional magnetic systems presents itself as one of the most promising candidates for the construction of nanodevices, useful for storing data, and for the construction of reading and writing magnetic heads. The vortex appears as the ground state of a magnetic nanodisk whose magnetic moments interact via dipole-dipole potential?. In this work it is investigated the conditions for the formation of vortices in nanodisks in triangular, square, and hexagonal lattices as a function of the size of the lattice and of the strength of the dipole interaction D. Our results show that there is a transition line separating the vortex state from a capacitor like state. This line has a finite size scaling form depending on the size, L, of the system as Dc=D0 +1/A(?1+B*L^2)?. This behavior is obeyed by the three types of lattices. Inside the vortex phase it is possible to identify two types of vortices separated by a constant, D=Dc, line: An in-plane and an out-of-plane vortex. We observed that the out-of-plane phase does not appear for the triangular lattice. In a two layer system the extra layer of dipoles works as an effective out-of-plane anisotropy inducing a large S^z component at the center of the vortex. Also, we analyzed the mechanism for switching the out-of-plane vortex component. Contrary to some reported results, we found evidences that the mechanism is not a creation-annihilation vortex anti-vortex process.
A lattice model of 3He - 4He mixtures which takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom of 4He is studied in the molecular-field approximation and by Monte Carlo simulations in three dimensions. In contrast to its two-dimensional version, for reasonable values of the interaction parameters the resulting phase diagram resembles that observed experimentally for 3He - 4He mixtures, for which phase separation occurs as a consequence of the superfluid transition. The corresponding continuum Ginzburg-Landau model with two order parameters describing 3He- 4He mixtures near tricriticality is derived from the considered lattice model. All coupling constants appearing in the continuum model are explicitly expressed in terms of the mean concentration of 4He, the temperature, and the microscopic interaction parameters characterizing the lattice system.
The critical behaviour of statistical models with long-range interactions exhibits distinct regimes as a function of $rho$, the power of the interaction strength decay. For $rho$ large enough, $rho>rho_{rm sr}$, the critical behaviour is observed to coincide with that of the short-range model. However, there are controversial aspects regarding this picture, one of which is the value of the short-range threshold $rho_{rm sr}$ in the case of the long-range XY model in two dimensions. We study the 2d XY model on the {it diluted} graph, a sparse graph obtained from the 2d lattice by rewiring links with probability decaying with the Euclidean distance of the lattice as $|r|^{-rho}$, which is expected to feature the same critical behavior of the long range model. Through Monte Carlo sampling and finite-size analysis of the spontaneous magnetisation and of the Binder cumulant, we present numerical evidence that $rho_{rm sr}=4$. According to such a result, one expects the model to belong to the Berezinskii-Kosterlitz-Thouless (BKT) universality class for $rhoge 4$, and to present a $2^{nd}$-order transition for $rho<4$.
We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.
The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier WL implementations, by handling the final stage of the WL process as an entropic sampling scheme, appropriate for the recording of the required two-parametric histograms. We test the accuracy of the proposed extrapolation scheme and then apply it to study the size-shift behavior of the phase diagram of the 3D bimodal RFIM. We present a finite-size converging approach and a well-behaved sequence of estimates for the critical disorder strength. Their asymptotic shift-behavior yields the critical disorder strength and the associated correlation lengths exponent, in agreement with previous estimates from ground-state studies of the model.
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