A Blume-Capel spin glass with competing crystal-field interactions on a hierarchical lattice

Renormalization-group methods are used with a hierarchical lattice to model a Blume-Capel spin glass with annealed vacancies and competing crystal-field interactions. The strength of competing cross-link interactions is progressively increased as the effects, upon the phase diagrams, are investigated. A series of phase diagrams have been produced, sinks interpreted, and critical exponents calculated for higher order transitions.     

Extraction of the resonance parameters at finite times

In this paper we propose a model-independent method to extract the resonance parameters on the lattice directly from the Euclidean 2-point correlation functions of the field operators at finite times. The method is tested in case of the two-point function of the Δ-resonance, calculated at one loop in Small Scale Expansion. Further, the method is applied to a 1+1$1+1$-dimensional model with two coupled Ising spins and the results are compared with earlier ones obtained by using Lüscher's approach.     

The Inversion Relation and the Dilute A3, 4, 6 Eigenspectrum

On the basis of the result obtained by applying Baxter's exact perturbative approach to the dilute A₃ model to give the E₈ mass spectrum, the dilute A_L inversion relation was used to predict the eigenspectra in the L=4 and L=6 cases (corresponding to E₇ and E₆ respectively). In calculating the next-to-leading term in the correlation lengths, or equivalently masses, the inversion relation condition gives a surprisingly simple result in all three cases, and for all masses.     

连续平均场Ising模型的显式差分格式

将离散的平均场Ｉｓｉｎｇ模型转换为连续的模型，给出了显式差分格式。利用有界延拓法，证明了差分解的收敛性与稳定性。最后通过数值例子说明了此格式的可信性。     

The spin-

We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic planeH ² in the same sense asZ ^d is a discretization ofR ^d . We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.     

Ising models on hyperbolic graphs

We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic planeH ² in the same sense asZ ^d is a discretization ofR ^d . We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.     

On Criticality for Competing Influences of Boundary and External Field in the Ising Model

We continue a study of Schonmann (1994), Schonmann and Shlosman (1996), and Greenwood and Sun (1997) regarding the competing influences of boundary conditions and external field for the Ising model. We find a critical point B ₀ in the competing influences for low temperature in dimension d 2A7E; 2.     

The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L=4,6,8,10. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T_C=10.838(1), T_C=10.836(20) and T_C=10.835(1) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T_C=10.835(5). The value obtained for the critical exponent of the specific heat, i.e., =0.012(2) is also in agreement with =0 predicted by the theory.     

Exact equilibrium shapes of Ising crystals on triangular/honeycomb lattices

The anisotropic surface tension for an Ising system below the critical point on a triangular or a honeycomb lattice can be computed through duality. Using the Wulff construction, the equilibrium shape of a crystal (droplet of one phase inside a sea of the other) is found. An exact and simple equation for this shape is derived.