Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice

The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality \(\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d\). Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.     

Ground State of an Antiferromagnetic Three-State Potts Model on a Triangular Lattice with Competing Interactions

The ground state of the spin structures described by an antiferromagnetic three-state Potts model on a triangular lattice is studied with allowance for the next-nearest neighbors. The numerical data obtained by the Monte Carlo method are used to reveal the ranges of ordered and disordered phases in these structures.     

Phase Transitions in the Two-Dimensional Slightly Diluted Five-Vertex Potts Model

Physics of the Solid State - Phase transitions in the two-dimensional slightly diluted Potts model on a square lattice at q = 5 have been studied using the computer simulation method. The systems...     

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Physics of the Solid State - The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems...     

Theory of Photo-emission from the Two-Dimensional t-J Model on a Triangular Lattice

The electron spectral function, the electron dispersion, and the electron density of states of the two-dimensional t-J model on a triangular lattice are studied within the selfconsistent fermion-spin mean-field theory. It is shown that there is a gap in the electron dispersions, and the global features of the electron spectral function is qualitatively similar to the result of the t-J model on a square lattice.     

Frustrated Potts Model with Spin States Number q = 4 on a Triangular Lattice

Journal of Experimental and Theoretical Physics - The Monte Carlo Wang–Landau algorithm was used to study the magnetic structures of the ground state and the thermodynamic properties of the...     

High-Frequency Hoping Conductivity in a Two-Dimensional Antiferromagnetic Lattice

The optical properties of two-dimensional antiferromagnetic lattice were etudied through the theoretical calculation of the high-frequency hoping conductivity in a spin-deneity-wave background. The effect of the strong spin correlation in the bag excitation region on the conductivity is diecueeed. Calculations have been made under the mean-field approximation including self-energy and vertex contributions.     

Exact Potts Model Partition Functions for Strips of the Triangular Lattice

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form Z(G,q,v)= $\sum _{j = 1}^{N_{Z,G,\lambda } }$ c _z,G,j (λ _z,G,j ) ^m-1. We give general formulas for N _Z,G,j and its specialization to v=?1 for arbitrary L. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite triangular lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus ${\mathcal{B}}$ , arising as the accumulation set of partition function zeros as m→∞, in the q plane for fixed v and in the v plane for fixed q. Explicit results for partition functions are given in the text for L=3 (free) and L=3, 4 (cylindrical), and plots of partition function zeros and their asymptotic accumulation sets are given for L up to 5. A new estimate for the phase transition temperature of the q=3 Potts antiferromagnet on the 2D triangular lattice is given.     

Quantum Oscillations of Magnetization in Antiferromagnetic Semimetals on a Triangular Lattice

The specific features of magnetization in antiferromagnetic semimetals with a low charge carrier density on a triangular lattice in a high magnetic field are studied. It is demonstrated that the well-known plateau in the magnetic field dependence of the magnetization manifesting itself in the subsystem of localized S = 1/2 spins is actually not strictly horizontal but has a slight positive slope. It is found that an abrupt change in the frequency of quantum oscillations of the magnetization in the itinerant subsystem should be observed at the magnetic field values corresponding to the edges of this plateau owing to the strong s–d(f) exchange coupling.     

三角晶格二维光子晶体的横磁模特性

基于平面波展开法,以介电常数分别为1F/m和12F/m的物质构成三角晶格二维光子晶体,改变空气孔半径r与晶格常数a之间的大小,数值模拟得到了三角晶格二维光子晶体横磁模带隙,当r=.4α时形成三处三角晶格二维光子晶体横磁模的带隙,其中最大三角晶格二维光子晶体横磁模带隙出现在0.6766—0.8000Hz,差值为0.1234Hz。研究结论为光子晶体器件的制作提供参考。     

The High Temperature Ising Model on the Triangular Lattice is a Critical Bernoulli Percolation Model

We define a new percolation model by generalising the FK representation of the Ising model, and show that on the triangular lattice and at high temperatures, the critical point in the new model corresponds to the Ising model. Since the new model can be viewed as Bernoulli percolation on a random graph, our result makes an explicit connection between Ising percolation and critical Bernoulli percolation, and gives a new justification of the conjecture that the high temperature Ising model on the triangular lattice is in the same universality class as Bernoulli percolation.     

Ground State Entropy of the Potts Antiferromagnet on Triangular Lattice Strips

We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L_x vertices and of width L_y vertices and, in the L_x→∞ limit, the exponent of the ground state entropy, W=e^S₀/k_B. The strips considered, with their boundary conditions (BC), are (a) (FBC_y, PBC_x) = cyclic for L_y=3, 4, (b) (FBC_y, TPBC_x) = Möbius, L_y=3, (c) (PBC_y, PBC_x) = toroidal, L_y=3, (d) (PBC_y, TPBC_x) = Klein bottle, L_y=3, (e) (PBC_y, FBC_x) = cylindrical, L_y=5, 6, and (f) (FBC_y, FBC_x) = free, L_y=5, where F, P, and TP denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2πL_x/3) for case (c). The continuous locus of points where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices.     

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae ^{2 p} (1+a ₁ e ^– + ...) as , with p1. The staggered susceptibility behaves as _stagg ^5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.     

二维三角光学格子中的PT光孤子研究

研究了基于自散焦克尔非线性的PT对称三角格子中双峰光孤子的存在性及稳定性。采用改进的平方算子法(MSOM)迭代计算出孤子的数值解,发现双峰之间具有相同相位的双峰光孤子存在于第一带隙,并且可以在某个范围内稳定传输。由傅里叶配点法得到的线性稳定性与非线性模拟传输的结果是一致的。此外,这种PT对称的双峰光孤子对入射角度非常敏感,从不同角度入射的光孤子具有不同的传输特性。     

The Critical Behavior of the Antiferromagnetic Ising Model with Long-Range Interaction Effects

In this paper, the antiferromagnetic Ising model with ferromagnetic long-range interaction is modeled by the Monte Carlo method. The case of ferromagnetic long-range forces decreasing by a power law is considered. The dependence of the phase-transition temperature on long-range interaction parameters is obtained. The phase diagram was constructed at different values of long-range interaction parameters. Conditions for the existence of the frustrated state of the system were revealed.     

Critical Properties in the Ising Model on a Triangular Lattice with the Variable Interlayer Exchange Interaction

Physics of the Solid State - Phase transitions and critical and thermodynamic properties of the three-dimensional antiferromagnetic Ising model on a layered triangular lattice with variable...     

Phase Diagram of the Antiferromagnetic Heisenberg Model on a Cubic Lattice

Phase transitions in the antiferromagnetic Heisenberg model on a cubic lattice with intralayer next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. The magnitude of next-nearest neighbor interactions varies in the range of 0.0 ≤ r ≤ 1.0. The characteristics of the phase transitions are analyzed by the histogram and Binder cumulant techniques. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. In this model, it is found that the intralayer next-nearest neighbor interactions do not change the order of the phase transition.

     

The Critical Behavior of the Ising Model on Union Jack Lattice

In this paper, we have investigated the critical behavior of the ferromagnetic Ising model on union jack lattice. The model is equivalent to the eight-vertex model which can be solved as a free fermion model with the free fermion approximation. The critical exponents have been obtained as aα = α = 0, β = β'= 0.125, γ = γ' = 0.875 and δ = δ' = 8.     

An Analytical Study of Three-State Potts Model on Lattice

We investigate the phase structure of the three-state Potts model by the variational cumulant expansion approach. It is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.