PHASE BOUNDARY AND UNIVERSALITY OF THE TRIANGULAR LATTICE ANTIFERROMAGNETIC ISING MODEL

1992 ◽  
Vol 06 (17) ◽  
pp. 2913-2924 ◽  
Author(s):  
JAE DONG NOH ◽  
DOOCHUL KIM
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Phase Boundary ◽  
Triangular Lattice ◽  
Central Charge ◽  
Universality Class ◽  
Zero Field ◽  
Crossover Effect ◽  
Matrix Methods ◽  
Antiferromagnetic Ising Model

Transfer matrix methods are used to locate accurate phase boundary of the triangular lattice antiferromagnetic Ising model in magnetic field. Universal quantities such as the central charge and the first few scaling dimensions are obtained along the phase boundary except near the zero field point where the crossover effect degrades convergence. Numerical results are fully consistent with the operator content of the 3-state Potts model indicating that whole phase boundary belongs to the 3-state Potts universality class.

ISING MODEL IN THE MAGNETIC FIELD iπkT/2

1988 ◽  
Vol 02 (03n04) ◽  
pp. 471-481 ◽  
Author(s):  
K. Y. LIN ◽  
F. Y. WU
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Ising Model ◽  
Zero Field ◽  
Two Dimensional ◽  
Anisotropic Interactions ◽  
The Magnetic Field ◽  
Explicit Expressions

It is shown that the free energy and the magnetization of an Ising model in the magnetic field H = iπkT/2 can be obtained directly from corresponding expressions of these quantities in zero field, provided that the latter are known for sufficiently anisotropic interactions. Using this approach we derive explicit expressions of the free energy and the magnetization at H = iπkT/2 for a number of two-dimensional lattices.

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

1983 ◽  
Vol 61 (11) ◽  
pp. 1515-1527 ◽  
Author(s):  
James Glosli ◽  
Michael Plischke
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Ising Model ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbor ◽  
Universality Class ◽  
Energy Functional ◽  
First Order ◽  
Universality Classes

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

Low-Temperature Behaviors of Antiferromagnetic Ising Model of Infinite-Spin on Triangular Lattice

1992 ◽  
Vol 61 (9) ◽  
pp. 3114-3124 ◽  
Author(s):  
Tsuyoshi Horiguchi ◽  
Ojiro Nagai ◽  
Seiji Miyashita ◽  
Yukio Miyatake ◽  
Yoshiki Seo
Keyword(s):  
Ising Model ◽  
Low Temperature ◽  
Triangular Lattice ◽  
Antiferromagnetic Ising Model

scholarly journals Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 862
Author(s):  
Ildus F. Sharafullin ◽  
Hung T. Diep
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Triangular Lattice ◽  
Applied Field ◽  
Zero Field ◽  
Ferroelectric Films ◽  
Dm Interaction ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magneto–electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto–electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

Sign in / Sign up

Export Citation Format

Share Document