scholarly journals QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J1–J2 MODEL ON THE CUBIC LATTICE

2013 ◽  
Vol 27 (26) ◽  
pp. 1350162 ◽  
Author(s):  
OCTAVIO D. R. SALMON ◽  
NUNO CROKIDAKIS ◽  
MINOS A. NETO ◽  
IGOR T. PADILHA ◽  
J. ROBERTO VIANA ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Ising Model ◽  
Effective Field Theory ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Universality Class ◽  
Continuous Phase ◽  
Effective Field ◽  
Cubic Lattice ◽  
Plane Temperature

The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic (F) nearest-neighbor interactions (J1) and antiferromagnetic (AF) next-nearest-neighbor couplings (J2) are analyzed in the plane temperature versus α, where α = J2/|J1| is the frustration parameter. We used the original Wang–Landau sampling (WLS) and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature re-entrant behavior, observed in the frontier separating the F and the collinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo (MC) simulations of the model. In addition, our results indicate that the continuous phase transition between the F and the paramagnetic (P) phases, that occurs for 0.0 ≤α< 0.25, belongs to the universality class of the three-dimensional pure Ising Model.

scholarly journals The magnetic susceptibility on the transverse antiferromagnetic Ising model: Analysis of the reentrant behavior

2016 ◽  
Vol 30 (17) ◽  
pp. 1630011
Author(s):  
Minos A. Neto ◽  
J. Ricardo de Sousa ◽  
Igor T. Padilha ◽  
Octavio D. Rodriguez Salmon ◽  
J. Roberto Viana ◽  
...  
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Magnetic Susceptibility ◽  
Ising Model ◽  
Magnetic Fields ◽  
Effective Field Theory ◽  
Three Dimensional ◽  
Effective Field ◽  
Antiferromagnetic Ising Model ◽  
Reentrant Phenomena

We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal [Formula: see text] and transverse [Formula: see text] magnetic fields by using the effective-field theory (EFT) with finite cluster [Formula: see text] spin (EFT-1). We analyzed the behavior of the magnetic susceptibility to investigate the reentrant phenomena that we have seen in the same phase diagram previously obtained in other papers. Our results shows the presence of two divergences in the susceptibility that indicates the existence of a reentrant behavior.

scholarly journals 3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY

2005 ◽  
Vol 16 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
MELANIE SCHULTE ◽  
CAROLINE DROPE
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
External Field ◽  
Nearest Neighbor ◽  
Monte Carlo Study ◽  
Universality Class ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Binder Cumulant

We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

scholarly journals THE CLUSTER PROCESSOR: NEW RESULTS

1999 ◽  
Vol 10 (06) ◽  
pp. 1137-1148 ◽  
Author(s):  
HENK W. J. BLÖTE ◽  
LEV. N. SHCHUR ◽  
ANDREI L. TALAPOV
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Universality Class ◽  
Scaling Exponent ◽  
Monte Carlo Data ◽  
Correction To Scaling ◽  
Purpose Computer ◽  
Special Purpose Computer

We present a progress report on the Cluster Processor, a special-purpose computer system for the Wolff simulation of the three-dimensional Ising model, including an analysis of simulation results obtained thus far. These results allow, within narrow error margins, a determination of the parameters describing the phase transition of the simple-cubic Ising model and its universality class. For an improved determination of the correction-to-scaling exponent, we include Monte Carlo data for systems with nearest-neighbor and third-neighbor interactions in the analysis.

scholarly journals Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

2018 ◽  
Vol 32 (32) ◽  
pp. 1850390
Author(s):  
Minos A. Neto ◽  
J. Roberto Viana ◽  
Octavio D. R. Salmon ◽  
E. Bublitz Filho ◽  
José Ricardo de Sousa
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Effective Field ◽  
The Body ◽  
Bravais Lattice ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

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