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 $20\text{−}\text{year}$-long controversial issue.

In this paper, we show, 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.

We study by extensive Monte Carlo (MC) simulations and analytical Green’s 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 nonlinear 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 calculations 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.

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the past few decades. A theoretical model was proposed by [T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the model of Vicsek et al., in this paper, we consider a group of animals as particles moving freely in a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle $\phi =\varphi /2$ $(\varphi$ is called the angle of view) of a circle centered at its position of radius $R$. We obtained a phase diagram in the space $\left(\phi ,{\eta }_c\right)$ with ${\eta }_c$ being the critical noise. We show that the phase transition exists only in the case of a wide view's angle $\phi \ge 0.5\pi$. The flocking of animals is a universal behavior of the species of prey but not the one of the predator. Our simulation results are in good agreement with experimental observation [C. Beccoa et al., Physica A 367, 487 (2006)].

We study the effects of frustration in an antiferromagnetic film with a face- centered cubic (FCC) lattice structure with the Heisenberg spin model including an Ising-like anisotropy. Monte Carlo (MC) simulations have been used to study the 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 Js 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. We study here how the physical properties vary as the surface bond strength changes at a fixed film thickness. The nature of the phase transition is also studied by a histogram technique. We have also used the Green's function (GF) method for the quantum counterpart model. The results at low temperature (T )s how 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.