Three-state majority-vote model on square lattice

Here, a non-equilibrium model with two states (−1,+1) and a noise q on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as the majority-vote model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the majority-vote model for a version with three states, now including the zero state, (−1,0,+1) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 (−1,0,+1) and spin-1/2 Ising model and also agree with majority-vote model proposed for M.J. Oliveira (1992). The exponent ratio obtained for our model was γ/ν=1.77(3), β/ν=0.121(5), and 1/ν=1.03(5). The critical noise obtained and the fourth-order cumulant were q_c=0.106(5) and U^∗=0.62(3).     

Uniaxially anisotropic antiferromagnets in a field on a square lattice

Classical uniaxially anisotropic Heisenberg and XY antiferromagnets in a field along the easy axis on a square lattice are analysed, applying ground state considerations and Monte Carlo techniques. The models are known to display antiferromagnetic and spin-flop phases. In the Heisenberg case, a single-ion anisotropy is added to the XXZ antiferromagnet, enhancing or competing with the uniaxial exchange anisotropy. Its effect on the stability of non-collinear structures of biconical type is studied. In the case of the anisotropic XY antiferromagnet, the transition region between the antiferromagnetic and spin-flop phases is found to be dominated by degenerate bidirectional fluctuations. The phase diagram is observed to resemble closely that of the XXZ antiferromagnet without single-ion anisotropy.     

Finite-size scaling of the three-state Potts model on a simple cubic lattice

Finite-size scaling is studied for the three-state Potts model on a simple cubic lattice. We show that the specific heat and the magnetic susceptibility scale accurately as the volume. The correlation length exhibits behaviors expected for a genuine first-order transition; the one extracted from the unsubtracted correlation function shows a characteristic finite-size behavior, whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point.     

Anisotropy of the interface tension of the three-dimensional Ising model

We determine the interface tension for the 100, 110 and 111 interface of the simple cubic Ising model with nearest-neighbour interaction using novel simulation methods. To overcome the droplet/strip transition and the droplet nucleation barrier we use a newly developed combination of the multimagnetic algorithm with the parallel tempering method. We investigate a large range of inverse temperatures to study the anisotropy of the interface tension in detail.     

Conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice

A conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice is investigated by exact calculations. An importance of the electron hopping and spatial orientation of the electric field upon a magnetoelectric effect is examined in detail. A critical temperature may display one or two consecutive round maxima as a function of the electric field. Although the rotating magnetoelectric effect (RME) does not affect the ground-state ordering, the pronounced RME is found close to a critical temperature of continuous phase transition. It is shown that RME is amplified upon strengthening of the electric field, which additionally supports thermal fluctuations in destroying a spontaneous antiferromagnetic long-range order.     

Ground state properties of a spin-3/2 model on a decorated square lattice

We present the construction of an optimum ground state for a quantum spin-3/2 antiferromagnet. The spins reside on a decorated square lattice, in which the basis consists of a plaquette of four sites. By using the vertex state model approach we generate the ground state from the same vertices as those used for the corresponding ground state on the hexagonal lattice. The properties of these two ground states are very similar. Particularly there is also a parameter-controlled phase transition from a disordered to a Néel ordered phase. In the regime of this transition, ground state properties can be obtained from an integrable classical vertex model. Received 28 June 1999     

Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J₁ on nearest neighbour and J₂ on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the criticalpoint at J₂ = J₁/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J₂ > J₁/2.     

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

Damage spreading in a driven lattice gas model

We studied damage spreading in a Driven Lattice Gas (DLG) model as a function of the temperature T$T$, the magnitude of the external driving field E$E$, and the lattice size. The DLG model undergoes an order–disorder second-order phase transition at the critical temperature _Tc(E)$T_c\left(E\right)$, such that the ordered phase is characterized by high-density strips running along the direction of the applied field; while in the disordered phase one has a lattice-gas-like behavior. It is found that the damage always spreads for all the investigated temperatures and reaches a saturation value _Dsat$D_{sat}$ that depends only on T$T$. _Dsat$D_{sat}$ increases for T<_Tc(E=∞)$T<T_c(E=\infty )$, decreases for T>_Tc(E=∞)$T>T_c(E=\infty )$ and is free of finite-size effects. This behavior can be explained as due to the existence of interfaces between the high-density strips and the lattice-gas-like phase whose roughness depends on T$T$. Also, we investigated damage spreading for a range of finite fields as a function of T$T$, finding a behavior similar to that of the case with E=∞$E=\infty$.     

A non-thermal lattice gas model for a dimer-trimer reaction on a catalytic surface: A computer simulation study

The kinetics of an irreversible dimer-trimer reaction of the type 3A₂ + 2B₃ → 6AB have been studied using a non-thermal (precursor mechanism) model on a square as well as on a hexagonal lattice surface by Monte Carlo simulation. When the range of the precursors (A atoms) is increased, the model gives production rates (reactive window widths) that are quite large as compared with those for thermal (Langmuir-Hanshelwood mechanism) model. The phase diagrams qualitatively resemble with the standard ZGB model except that the continuous transition point is eliminated when the range of the precursors is extended up to the third nearest neighbourhood. The diffusion of A atoms on the surface as well as their desorption from the surface with a certain probability is also considered to see their effects on the reaction mechanism.     

Monte Carlo simulations of electromagnetically induced transparency in a square lattice of Rydberg atoms

We study the steady optical response of a square lattice in which all trapped atoms are driven by a probe and a coupling fields into the ladder configuration of electromagnetically induced transparency(EIT). It turns out to be a manybody problem in the presence of van der Waals(vd W) interaction among atoms in the upmost Rydberg state, so Monte Carlo(MC) calculation based on density matrix equations have been done after introducing a sufficiently large cut-off radius. It is found that the absorption and dispersion of EIT spectra depends critically on a few key parameters like lattice dimension, unitary vd W shift, probe Rabi frequency, and coupling detuning. Through modulating these parameters, it is viable to change symmetries of the absorption and dispersion spectra and control on demand depth and position of the transparency window. Our MC calculation is expected to be instructive in understanding many-body quantum coherence effects and in manipulating non-equilibrium quantum phenomena by utilizing vd W interactions of Rydberg atoms.     

A seed-diffusion model for tropical tree diversity patterns

Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple statistical physics process, namely the diffusion of seeds. The model has three parameters: the speciation rate, the size of the meta-community in which the studied tree-community is embedded, and the average surviving time of the seeds. By extensive computer simulations we aim towards the reproduction of relevant statistical measures derived from the experimental data of the Barro Colorado Island tree census in 1995. The first two parameters of the model are fixed to known values, characteristic of the studied community, thus obtaining a model with only one freely adjustable parameter. As a result of this, the average number of species in the considered territory, the relative species abundance distribution, the species–area relationship and the spatial auto-correlation function of the individuals in abundant species are simultaneously fitted with only one parameter which is the average surviving time of the seeds.     

Monte Carlo study of the critical behavior of pure and site-diluted Ising ferro-and ferrimagnets

Monte Carlo simulations are performed for pure and site-diluted Ising ferro- and ferrimagnets on a simple cubic lattice with up to 40³ sites and with impurity concentrationx. For the diluted ferromagnet (x=0.2) the exponent= 0.392±0.03 is definitely larger than the pure model value of=0.304±0.03. In contrast, for ferrimagnetic systems (x=0, 0.1, 0.2) the values appear to be independent ofx and within the error limits consistent with the value for the pure ferromagnet, possibly because the width of the asymptotic random critical regime (or of the crossover regime) is even smaller than in the case of ferromagnets.     

Exact and Monte Carlo computations on a lattice model for change of conformation of a polymer

Conformational changes of linear polymers are studied by means of dynamic lattice models. The relaxation rates for the following four parameters describing the conformation of the polymer are studied for various polymer lengths: the square of the end-to-end distance, the square of the radius of gyration, thex component of the end-to-end vector, and the number of windings.In the most realistic models the relaxation rates for the first three of the above-mentioned properties decrease approximately proportional to the square of the number of monomers in agreement with the well-known Rouse model, while the relaxation of the winding number appears to be independent of the polymer length. The long-range interactions due to excluded volume restrictions are found to be of only minor importance compared to the rules presented for the local movements of the polymer segments.The results are obtained by diagonalizing the Markov matrix forn = 3, 4, 5, and 6 and by Monte Carlo simulation forn = 8, 16, 32, 64, and 128, wheren is the number of monomers.     

Monte Carlo Simulation of the Non-universal Short-Time Behavior for a Kinetic 2-D Ising Model

The short-time dynamic process for the two-dimensional Ising model with the nearest-neighbor coupling and the next-nearest-neighbor antiferromagnetic coupling in the critical domain is simulated by the Monte Carlo method. From the power law behavior of the initial order increase, the critical points and the initial dynamic exponent θ are determined.     

Critical wetting in the square Ising model with a boundary field

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH ₁ acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.Alexander von Humboldt-Fellow     

Ground state phase diagram of a spin-2 antiferromagnet on the square lattice

We use the vertex state model approach to construct optimum ground states for a large class of quantum spin-2 antiferromagnets on the square lattice. Optimum ground states are exact ground states of the model which minimize all local interaction operators. The ground state contains two continuous parameters and exhibits a second order phase transition from a disordered phase with exponentially decaying correlation functions to a Néel ordered phase. The behaviour is very similar to that of the corresponding ground state of a quantum spin-3/2 model on the hexagonal lattice, which has been investigated in an earlier paper. Received 8 April 1999     

Folding of lattice protein model chains with fixed ends

Using Monte Carlo simulations, we have studied the folding dynamics and thermodynamics of geometricall yconstrained lattice protein model chains. The constraints are realized by fixing one or both terminals of the chains. By comparing the results with that of the free-end chains, we find that the folding behaviours of the end-constralned chains are not completely similar to that of the free-end chains. Both kinds of constraints on the chain ends affect the folding dynamics of the chains: i.e., the folding rate, but not the thermodynamics. The thermodynamic behaviour of the one-end-fixed chains shows less difference from that of the free-end chains, while the thermodynamic behaviour of the two-end-fixed chains has obvious difference from that of the free-end chains. The origin of these differences comes from the differences of the ergodicitv of the chains in the conformational space.     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

Computer investigations of the three-dimensional Ising model

We have been studying the three-dimensional Ising model using some finite-size scaling ideas. The simulation is done by a fast microcanonical method. Here we present our results for the critical exponents and.