Thermodynamics of the Hubbard model on stacked honeycomb and square lattices

We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling.     

Phases of the infinite U Hubbard model on square lattices

We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n?0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states.     

Monte Carlo study of binary mixtures adsorbed on square lattices

The monolayer adsorption of interacting binary mixtures on 2D square lattices has been studied through grand canonical Monte Carlo simulation in the framework of the lattice-gas model. The process has been monitored through total and partial isotherms and differential heats of adsorption corresponding to both species of the mixture. Repulsive lateral interactions between the adsorbed particles have been considered, resulting in a rich variety of structural orderings in the adlayer. At the end of this work, the phase diagram characterizing the transitions occurring in the system has been determined. A nontrivial interdependence between the partial surface coverage of both species was observed and discussed.     

Percolation of dimers on square lattices

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=_Lx×_Ly$M=L_x\times L_y$ cells, with M$M$ varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν$\nu$, β$\beta$ and γ$\gamma$ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ$\gamma$) with respect to some numeric values available in the literature.     

Mixture of polymers on square lattices

We obtain the entropy per site of non-overlapping rigid polymers of different lengths and different absolute activities, distributed on square lattices. Exact solutions are obtained for lattices consisting of one, two and three infinite strips of equally spaced lattice sites (M=1,2,3). Technically, there are no difficulties in extending the calculations to any number of infinite strips. In the absence of any polymer-polymer or polymer-lattice interaction energy, the partition function per site is well behaved and, near close packing, is shown to be proportional to the absolute activity per site of the polymers. The results of the one-dimensional problem (one strip or M=1) form the basis of approximate solutions for several strips (M=2,3, etc) in terms of the molecular freedom per site at close packing.     

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.     

Phase separation and flux quantization in the doped quantum dimer model on square and triangular lattices

The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with Q=2e elementary charge quanta in transport properties.     

Majority rule at low temperatures on the square and triangular lattices

We consider the majority-rule renormalization group transformation applied to nearest neighbor Ising models. For the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low, then the transformation is not defined. We use the methods of van Enter. Fewrnández, and Sokal, who proved the renormalized measure is not Gibbsian for 7 by 7 blocks if the temperature is too low. For the triangular lattice we prove that a zero-temperature majorityrule transformation may be defined. The resulting renormalized Hamiltonian is local with 14 different types of interactions.     

Bond percolation with parallelism restriction on square lattices

As a simple approximation for the ±J spin glass we studied bond percolation on square lattices. However, two neighboring chains of ferromagnetic bonds are required for spins to be regarded as connected. We determine the percolation thresholdp _c =0.8282±0.0002 and the critical exponent =0.75 _–0.05 ^+0.02 for this specific percolation by means of Monte-Carlo simulation on square lattices (up to 150×150).     

Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices

Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.     

Memory-based prisoner’s dilemma on square lattices

We investigate the evolutionary prisoner’s dilemma with memory-based agents on a square lattice. By introducing memory effects into this game, we assume that individuals’ performance is evaluated in terms of the accumulative payoffs in their memories. It is shown that if individuals behave as their successful neighbors, then cooperation can be significantly promoted. The mechanism responsible for the promotion of cooperation is discussed in detail. We confirm that the promotion of cooperation induced by memory effects remains effective when a preferential selection rule or an asynchronous updating rule is employed. Our work may shed some new light on the study of evolutionary games in real-world situations where the effects of individuals’ memories play a key role in the evolution of cooperation.     

Dimers on square lattices: Orientation dependent activities

Past studies of a mixture of non-overlapping rigid polymers distributed on square lattices were limited to polymers having the same activity regardless of orientation. Here, we address the problem of a single species, dimers, possessing different activities depending on their orientation, in the absence of both dimer-dimer and dimer-lattice interaction energies. The lattices considered consist of two, three, four and five infinite strips of equally spaced lattice sites (M=2, 3, 4, and 5). We propose an improved approximation technique for the study of the statistics of this system of dimers distributed on the infinite two-dimensional lattice (M=∞).     

正三角形及正方形微光学腔模式特性研究

微谐振腔模式特性研究是利用微腔研制新型光电器件的基础．为了研制出能采用平面工艺制作的定向输出的微腔激光器，文章采用解析和数值模拟方法深入研究了正三角形及正方形光学微腔的模式特性，并得到与数值模拟结果符合非常好的解析场分布及模式波长．对正方形光学微腔，把模式组合成满足正方形对称性的场分布，发现其类WG模式只存在品质因子比它小一个数量级以上的偶然简并模式，因此正方形微腔有利于实现真正的单模工作．     

Mixed Ising ferrimagnets with next-nearest-neighbour couplings on square lattices

We study Ising ferrimagnets on square lattices with antiferromagnetic exchange couplings between spins of values S = 1/2 and 1 on neighbouring sites, couplings between S = 1 spins at next-nearest-neighbour sites of the lattice and a single-site anisotropy term for the S = 1 spins. Using mainly ground state considerations and extensive Monte Carlo simulations, we investigate various aspects of the phase diagram, including compensation points, critical properties and temperature-dependent anomalies. In contrast to previous belief, the next-nearest-neighbour couplings, when being of antiferromagnetic type, may lead to compensation points.     

An equation of state for the Maier-Saupe model of nematic liquid crystals

An equation of state is presented for the Maier-Saupe model of nematic liquid crystals. Its derivation is based on isotropic repulsion between spherical hard cores and anisotropic attractive forces.     

Hexagonal and square flux line lattices in CeCoIn5

Using small-angle neutron scattering, we have imaged the magnetic flux line lattice (FLL) in the d-wave heavy-fermion superconductor CeCoIn5. At low fields we find a hexagonal FLL. Around 0.6 T this undergoes what is most likely a first-order transition to square symmetry, with the nearest neighbors oriented along the gap node directions. This orientation of the square FLL is consistent with theoretical predictions based on the d-wave order parameter symmetry.     

Coadsorption of monomers and dimers with first neighbour interactions on square lattices

We model surface coadsorption on a square lattice infinite in length and of finite width M. The adsorbed species occupy either one site (monomers) or two nearest neighbour sites (dimers) and have first neighbour interactions. The quantities computer per site at thermal equilibrium are the entropy, the number of each species, and the numbers of first neighbours (monomer-monomer, dimer-dimer, monomer-dimer). Numerical results are obtained for M ≤ 5. Structural orderings are observed and the detailed analysis of the corresponding phase diagrams is presented. Following our analysis, the boundary lines between phases are found to be linear for all M, and their exact analytic expressions are obtained for arbitrary values of the interaction energies. A number of extrapolations for any value of M is possible leading to predictions on the infinite two-dimensional lattice.