Abstract:
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.

Abstract:
We show in this paper by using the Wang-Landau flat-histogram Monte Carlo method that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative renormalization group, putting an end to a long-standing controversial issue.

Abstract:
By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first-order, contrary to results of earlier MC simulations using old-fashioned methods. Our result lends support to the conclusion of a nonperturbative renormalization group performed on an effective Hamiltonian. It puts an end to a 20-year long controversial issue.

Abstract:
We study by extensive Monte Carlo (MC) simulations and analytical Green function (GF) method effects of frustrated surfaces on the properties of thin films made of stacked triangular layers of atoms bearing Heisenberg spins with an Ising-like interaction anisotropy. We suppose that the in-plane surface interaction $J_s$ can be antiferromagnetic or ferromagnetic while all other interactions are ferromagnetic. We show that the ground-state spin configuration is non linear when $J_s$ is lower than a critical value $J_s^c$. The film surfaces are then frustrated. In the frustrated case, there are two phase transitions related to disorderings of surface and interior layers. There is a good agreement between MC and GF results. In addition, we show from MC histogram calculation that the value of the ratio of critical exponents $\gamma/\nu$ of the observed transitions is deviated from the values of two and three Ising universality classes. The origin of this deviation is discussed with general physical arguments.

Abstract:
In the bulk state, the Ising 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 (MC) simulations, we show that the transition remains first order down to a thickness of four FCC cells. 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 (GS) 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 $T_C$ while interior spins become disordered at a lower temperature $T_D$. 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 2D Ising universality class. We also show results obtained from the Green's function method. Discussion is given.

Abstract:
We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We observe that in the same range of varying thickness the deviation of the exponent $\nu$ is rather small, while exponent $\beta$ suffers a larger deviation. We explain these deviations using the concept of "effective" exponents suggested by Capehart and Fisher in a finite-size analysis. The shift of the critical temperature with the film thickness obtained here by MC simulation is in an excellent agreement with their prediction.

Abstract:
We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We observe that in the same range of varying thickness the deviation of the exponent $\nu$ is very small from its 2D value, while exponent $\beta$ suffers a larger deviation. Moreover, as long as the film thickness is fixed, i. e. no finite size scaling is done in the $z$ direction perpendicular to the film, the 3D values of the critical exponents cannot be attained even with very large (but fixed) thickness. The crossover to 3D universality class cannot therefore take place without finite size scaling applied in the $z$ direction, in the limit of numerically accessible thicknesses. From values of exponent $\alpha$ obtained by MC, we estimate the effective dimension of the system. We conclude that with regard to the critical behavior, thin films behave as systems with effective dimension between 2 and 3.

Abstract:
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.

Abstract:
We propose a new model in order to study behaviors of self-organized system such as a group of animals. We assume that the individuals have two degrees of freedom corresponding one to their internal state and the other to their external state. The external state is characterized by its moving orientation. The rule of the interaction between the individuals is determined by the internal state which can be either in the non-excited state or in the excited state. The system is put under a source of external perturbation called "noise". To study the behavior of the model with varying noise, we use the Monte-Carlo simulation technique. The result clearly shows two first-order transitions separating the system into three phases: with increasing noise, the system undergoes a phase transition from a dilute disordered phase to an ordered compact phase and then to the disordered dispersed phase. These phases correspond to behaviors of animals: uncollected state at low noise, flocking at medium noise and runaway at high noise, respectively.

Abstract:
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.