First-Order Transition in XY Fully Frustrated Simple Cubic Lattice

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the XY spin model. This system is the Villain's model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than twenty years

Descent methods for Nonnegative Matrix Factorization

In this paper, we present several descent methods that can be applied to nonnegative matrix factorization and we analyze a recently developped fast block coordinate method called Rank-one Residue Iteration (RRI). We also give a comparison of these different methods and show that the new block coordinate method has better properties in terms of approximation error and complexity. By interpreting this method as a rank-one approximation of the residue matrix, we prove that it \emph{converges} and also extend it to the nonnegative tensor factorization and introduce some variants of the method by imposing some additional controllable constraints such as: sparsity, discreteness and smoothness.Comment: 47 pages. New convergence proof using damped version of RRI. To appear in Numerical Linear Algebra in Signals, Systems and Control. Accepted. Illustrating Matlab code is included in the source bundl

Frustration Effects in Antiferromagnetic FCC Heisenberg Films

We study the effects of frustration in an antiferromagnetic film of FCC lattice with Heisenberg spin model including an Ising-like anisotropy. Monte Carlo (MC) simulations have been used to study thermodynamic properties of the film. We show that the presence of the surface reduces the ground state (GS) degeneracy found in the bulk. The GS is shown to depend on the surface in-plane interaction $J_s$ with a critical value at which ordering of type I coexists with ordering of type II. Near this value a reentrant phase is found. Various physical quantities such as layer magnetizations and layer susceptibilities are shown and discussed. The nature of the phase transition is also studied by histogram technique. We have also used the Green's function (GF) method for the quantum counterpart model. The results at low-$T$ show interesting effects of quantum fluctuations. Results obtained by the GF method at high $T$ are compared to those of MC simulations. A good agreement is observed.Comment: 11 pages, 19 figures, submitted to J. Phys.: Condensed Matte

Phase Transition in Heisenberg Fully Frustrated Simple Cubic Lattice

The phase transition in frustrated spin systems is a fascinated 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.Comment: submitted for publicatio

Effect of Disorder in the Frustrated Ising FCC Antiferromagnet: Phase Diagram and Stretched Exponential Relaxation

We study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration $p$ of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang-Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of $p$. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely $p\sim 0.01$, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small $p$ ($\simeq 5$). With increasing $p$, the system changes into a spin glass and then to a ferromagnetic phase when $p>0.65$. The phase diagram in the space ($T_c,p$) shows an asymmetry, unlike the case of the $\pm J$ Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor $b$ is equal to $\simeq 1/3$ at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models

Re-orientation Transition in Molecular Thin Films: Potts Model with Dipolar Interaction

We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper which correspond to the 3-state Potts model. The Hamiltonian of the system includes: (i) the exchange interaction $J_{ij}$ between nearest-neighbor sites $i$ and $j$ (ii) the long-range dipolar interaction of amplitude $D$ truncated at a cutoff distance $r_c$ (iii) a single-ion perpendicular anisotropy of amplitude $A$. We allow $J_{ij} =J_s$ between surface spins, and $J_{ij}=J$ otherwise. We show that the ground state depends on the the ratio $D/A$ and $r_c$. For a single layer, for a given $A$, there is a critical value $D_c$ below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature $T$ is increased, a re-orientation transition occurs near $D_c$: the low-$T$ in-plane ordering undergoes a transition to the perpendicular ordering at a finite $T$, below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio $J_s/J$. Surface and bulk order parameters as well as other physical quantities are shown and discussed.Comment: 7 pages, 11 figures, submitted for publicatio