H. T. Diep

Critical behavior of magnetic thin films

X. T. Pham Phu, V. Thanh Ngo and H. T. Diep a Laboratoire de Physique Théorique et Modélisation, CNRS-Université de Cergy-Pontoise, UMR 8089 2, Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France b Institute of Physics, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam c Asia Pacific Center for Theoretical Physics, Hogil Kim Memorial Building 5th floor, POSTECH, Hyoja-dong, Namgu, Pohang 790-784, Korea

Reexamination of the long-range Potts model: a multicanonical approach

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interactions 1/r(d+sigma), using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value sigma(c)(q) separating the first- and second-order regimes to two-digit precision within the range 3< or =q < or =9. We offer convincing numerical evidence supporting sigma(c)(q)<1.0 for all q, by virtue of an unusual finite-size effect, namely, finite-size scaling predicts a continuous transition in the thermodynamic limit, despite the first-order nature of the transition at finite size. A qualitative account in terms of correlation lengths is provided. Finally, we find the crossover between the LR and short-range regimes to occur inside a narrow window 1.0

Fast flat-histogram method for generalized spin models.

We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random walk in the energy space with collective updates controlled by the microcanonical temperature, our method yields dynamic exponents close to their ideal random-walk values, reduced equilibrium times, and very low statistical error in the density of states. The method can host any density of states estimation scheme, including the Wang-Landau algorithm and the transition matrix method. Our approach proves remarkably powerful in the numerical study of models governed by long-range interactions, where it is shown to reduce the algorithm complexity to that of a short-range model with the same number of spins. We apply the method to the -state Potts chains with power-law decaying interactions in their first-order regime; we find that conventional local-update algorithms are outperformed already for sizes above a few hundred spins. By considering chains containing up to spins, which we simulated in fairly reasonable time, we obtain estimates of transition temperatures correct to five-figure accuracy. Finally, we propose several efficient schemes aimed at estimating the microcanonical temperature.

Effect of dipolar interaction in molecular crystals.

In this paper we investigate the ground state and the nature of the transition from an orientational ordered phase at low temperature to the disordered state at high temperature in a molecular crystal. Our model is a Potts model which takes into account the exchange interaction J between nearest-neighbor molecules and a dipolar interaction between molecular axes in three dimensions. The dipolar interaction is characterized by two parameters: its amplitude D and the cutoff distance r(c). If the molecular axis at a lattice site has three orientations, say the x, y or z axes, then when D = 0, the system is equivalent to the 3-state Potts model: the transition to the disordered phase is known to be of first order. When D ≠ 0, the ground-state configuration is shown to be composed of two independent interpenetrating layered subsystems which form a sandwich whose periodicity depends on D and r(c). We show by extensive Monte Carlo simulation with a histogram method that the phase transition remains of first order at relatively large values of r(c).

Magnetic properties of two-dimensional nanodots: Ground state and phase transition

We study the effect of perpendicular single-ion anisotropy, −Asz2, on the ground-state structure and finite-temperature properties of a two-dimensional magnetic nanodot in presence of a dipolar interaction of strength D. By a simulated annealing Monte Carlo method, we show that in the ground state a vortex core perpendicular to the nanodot plane emerges already in the range of moderate anisotropy values above a certain threshold level. In the giant-anisotropy regime the vortex structure is superseded by a stripe domain structure with stripes of alternate domains perpendicular to the surface of the sample. We have also observed an intermediate stage between the vortex and stripe structures, with satellite regions of tilted nonzero perpendicular magnetization around the core. At finite temperatures, at small A, we show by Monte Carlo simulations that there is a transition from the the in-plane vortex phase to the disordered phase characterized by a peak in the specific heat and the vanishing vortex order pa...

SPIN TRANSPORT IN MAGNETICALLY ORDERED SYSTEMS: EFFECT OF THE LATTICE RELAXATION TIME

Spin resistivity R has been shown to result mainly from the scattering of itinerant spins with magnetic impurities and lattice spins. R is proportional to the spin–spin correlation so that its behavior is very complicated near and at the magnetic phase transition of the lattice spins. For the time being there are many new experimental data on the spin resistivity going from semiconductors to superconductors. Depending on materials, various behaviors have been observed. There is however no theory so far which gives a unified mechanism for the spin resistivity in magnetic materials. Recently, we have shown Monte Carlo results for different systems. We found that the spin resistivity is very different from one material to another. In this paper, we show for the first time how the dynamic relaxation time of the lattice spins affects the resistivity of itinerant spins observed in Monte Carlo simulation.

Crossover from first- to second-order transition in frustrated Ising antiferromagnetic films

In the bulk state, the Ising face-centered-cubic (fcc) antiferromagnet is fully frustrated and is known to have a very strong first-order transition. In this paper, we study the nature of this phase transition in the case of a thin film as a function of the film thickness. Using Monte Carlo simulations, we show that the transition remains first order down to a thickness of four fcc cells (eight atomic layers). It becomes clearly second order at a thickness of two fcc cells, i.e., four atomic layers. It is also interesting to note that the presence of the surface reduces the ground-state degeneracy found in the bulk. For the two-cell thickness, the surface magnetization is larger than the interior one. It undergoes a second-order phase transition at a temperature TC while interior spins become disordered at a lower temperature TD. This loss of order is characterized by a peak of the interior spins susceptibility and a peak of the specific heat which do not depend on the lattice size suggesting that either it is not a real transition or it is a Kosterlitz-Thouless nature. The surface transition, on the other hand, is shown to be of second order with critical exponents deviated from those of pure two-dimensional Ising universality class. We also show results obtained from the Greens function method. A discussion is given.

SPIN RESISTIVITY IN THE FRUSTRATED J1 - J2 MODEL

We study in this paper the resistivity encountered by Ising itinerant spins traveling in the so-called J1 - J2 frustrated simple cubic Ising lattice. For the lattice, we take into account the interactions between nearest-neighbors and next-nearest-neighbors, J1 and J2 respectively. Itinerant spins interact with lattice spins via a distance-dependent interaction. We also take into account an interaction between itinerant spins. The lattice is frustrated in a range of J2 in which we show that it undergoes a very strong first-order transition. Using Monte Carlo simulation, we calculate the resistivity ρ of the itinerant spins and show that the first-order transition of the lattice causes a discontinuity of ρ.

PHASE TRANSITION IN THE HEISENBERG FULLY-FRUSTRATED SIMPLE CUBIC LATTICE

The phase transition in frustrated spin systems is a fascinating subject in statistical physics. We show the result obtained by the Wang–Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple cubic lattice with the Heisenberg spin model. The degeneracy of the ground state of this system is infinite with two continuous parameters. We find a clear first-order transition in contradiction with previous studies which have shown a second-order transition with unusual critical properties. The robustness of our calculations allows us to conclude this issue putting an end to the 20-year long uncertainty.

Hybrid multicanonical cluster algorithm for efficient simulations of long-range spin models

An efficient, flat histogram Monte Carlo algorithm is proposed that simulates long-range spin models in the multicanonical ensemble with very low dynamic exponents and drastically reduced computational effort. The method combines a random-walk in energy space with cluster updates, where bond weights depend continuously on the lattice energy. Application to q-state Potts chains with power-law decaying interactions is considered. Lattice sizes as high as 216 spins, unattainable with conventional flat histogram algorithms, are investigated. Numerical results demonstrate the remarkable performance of the method over a wide spectrum of model parameters.