Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConstructing the Critical Curve for a Symmetric Two-Layer Ising Model
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A numerical method based on the transfer matrix method is developed to calculate the critical temperature of two-layer Ising ferromagnet with a weak inter-layer coupling. The reduced internal energy per site has been accurately calculated for symmetric ferromagnetic case, with the nearest neighbor coupling K1 = K2 = K (where K1 and K2 are the nearest neighbor interaction in the first and second layers, respectively) with inter layer coupling J. The critical temperature as a function of the inter-layer coupling J/K << 1, is obtained for very weak inter-layer interactions,J/K < 0.1 . Also a different function is given for the case of the strong inter-layer interactions (J/K > 1). The importance of these relations is due to the fact that there is no well tabulated data for the critical points versus J/K. We find the value of the shift exponent Phi = Gama is 1.74 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions.
rate research
Read More
A new finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature of anisotropic two-layer Ising ferromagnet, on strips of r wide sites of square lattices. The reduced internal energy per site has been accurately calculated for the ferromagnetic case, with the nearest neighbor couplings Kx, Ky (where Kx and Ky are the nearest neighbor interactions within each layer in the x and y directions, respectively) and with inter-layer coupling Kz, using different size-limited lattices. The calculated energies for different lattice sizes intersect at various points when plotted versus the reduced temperature. It is found that the location of the intersection point versus the lattice size can be fitted on a power series in terms of the lattice sizes. The power series is used to obtain the critical temperature of the unlimited two-layer lattice. The results obtained, are in good agreement with the accurate values reported by others.
The Binder cumulant at the phase transition of Ising models on square lattices with ferromagnetic couplings between nearest neighbors and with competing antiferromagnetic couplings between next--nearest neighbors, along only one diagonal, is determined using Monte Carlo techniques. In the phase diagram a disorder line occurs separating regions with monotonically decaying and with oscillatory spin--spin correlations. Findings on the variation of the critical cumulant with the ratio of the two interaction strengths are compared to related recent results based on renormalization group calculations.
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function $Z$ on an $Ltimes M$ square lattice, wrapped around a torus with aspect ratio $rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $rhoto 0$. Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $sigma$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.
The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the presence of a non-vanishing thermal field is found from finite-size scaling and the corresponding expression is fitted to the accurate perturbative transfer-matrix data calculations for the $Ltimes L$ square clusters with $Lleq 9$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
