scholarly journals Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

2021 ◽  
Vol 104 (14) ◽  
Author(s):  
Yi Hu ◽  
Patrick Charbonneau
Keyword(s):  
Transfer Matrix ◽  
Nearest Neighbor ◽  
Ising Models

CORRELATED REDUCED TRANSFER MATRIX APPROACH FOR ISING MODEL

2012 ◽  
Vol 26 (14) ◽  
pp. 1250085 ◽  
Author(s):  
TUNCER KAYA
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Nearest Neighbor ◽  
Ising Models ◽  
Critical Coupling ◽  
Average Magnetization ◽  
Ising Ferromagnets ◽  
Coupling Strengths ◽  
2D And 3D

In this paper we present a simple approximate transfer matrix method for 2D and 3D hyper cubic nearest neighbor Ising models with various coordination number z to calculate the corresponding critical coupling strengths Kc. The critical coupling strengths of the Ising ferromagnets are obtained quite accurately by simple improvements over the self-consistent correlated field (SCCF) approximation. The important physical effect included in this work is some of the fluctuation effects of the systems by the help of a reduced transfer matrix method. When used in combination with the accuracy of the average magnetization obtained from the SCCF approximation, this reduced transfer matrix method leads to estimate of Kc more accurate than those obtained from the Bethe–Peierls–Weiss approximation and also SCCF approximation. Therefore, we believe that the approach we refer to as the correlated reduced transfer matrix method is potentially very useful scheme for obtaining approximate values of the critical coupling strengths of the Ising models with a mathematically easy meaner.

scholarly journals Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit

2021 ◽  
Author(s):  
Giovanni Antinucci ◽  
Alessandro Giuliani ◽  
Rafael L. Greenblatt
Keyword(s):  
Nearest Neighbor ◽  
Scaling Limit ◽  
Ising Models ◽  
Infinite Volume ◽  
Effective Potentials ◽  
Volume Limit ◽  
Cylindrical Domains ◽  
Key Aspects ◽  
Infinite Volume Limit ◽  
Detailed Derivation

AbstractIn this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.

scholarly journals Contour Methods for Long-Range Ising Models: Weakening Nearest-Neighbor Interactions and Adding Decaying Fields

2018 ◽  
Vol 19 (8) ◽  
pp. 2557-2574 ◽  
Author(s):  
Rodrigo Bissacot ◽  
Eric O. Endo ◽  
Aernout C. D. van Enter ◽  
Bruno Kimura ◽  
Wioletta M. Ruszel
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Ising Models

Generation of low tehmperature series for Ising models with nearest and next nearest neighbor interactions

1976 ◽  
Vol 54 (16) ◽  
pp. 1646-1650 ◽  
Author(s):  
M. Plischke ◽  
C. F. S. Chan
Keyword(s):  
Low Temperature ◽  
Nearest Neighbor ◽  
Tricritical Point ◽  
Ising Models ◽  
Temperature Data ◽  
Temperature Series ◽  
Bcc Lattice ◽  
Special Cases ◽  
Ising Antiferromagnet ◽  
Ferromagnetic Interactions

We have generalized the code method of Sykes et al. and applied it to the Ising model with nearest and next nearest neighbor interactions. On the bcc lattice, we have obtained the first seven low temperature polynomials for arbitrary sign of the interactions. Special cases of this model are the Ising ferromagnet and the Ising antiferromagnet with next nearest neighbor ferromagnetic interactions. The latter system exhibits a tricritical point which we plan to study using our low temperature data and high temperature series to be obtained in the future.

Finite-size scaling of two-dimensional axial next-nearest-neighbor Ising models

1985 ◽  
Vol 31 (11) ◽  
pp. 7166-7170 ◽  
Author(s):  
Paul D. Beale ◽  
Phillip M. Duxbury ◽  
Julia Yeomans
Keyword(s):  
Nearest Neighbor ◽  
Finite Size ◽  
Ising Models ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling

Two one-dimensional Ising models with disorder points

1970 ◽  
Vol 48 (14) ◽  
pp. 1724-1734 ◽  
Author(s):  
John Stephenson
Keyword(s):  
Temperature Dependence ◽  
Short Range ◽  
Short Range Order ◽  
Nearest Neighbor ◽  
Ising Models ◽  
Zero Field ◽  
Interaction Energies ◽  
Pair Correlations ◽  
One Dimensional ◽  
Range Of Values

Pair correlations on two one-dimensional Ising models with next-nearest-neighbor interactions are calculated exactly. For an appropriate range of values of the interaction energies, each of these models exhibits a disorder point, at which the nature of the short-range order changes abruptly, and at which there is a cusp in the graph of range of order vs. temperature. The zero-field susceptibilities are calculated exactly, and are found to have quite smooth temperature dependence.

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