Honeycomb-lattice antiferromagnetic Ising model in a magnetic field

2006 ◽  
Vol 358 (4) ◽  
pp. 245-250 ◽  
Author(s):  
Seung-Yeon Kim
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Honeycomb Lattice ◽  
Antiferromagnetic Ising Model

CRITICAL POINT OF THE HONEYCOMB ANTIFERROMAGNETIC ISING MODEL IN A NONZERO MAGNETIC FIELD: FINITE-SIZE ANALYSIS

1990 ◽  
Vol 04 (04) ◽  
pp. 619-629 ◽  
Author(s):  
H. W. J. BLÖTE ◽  
F. Y. WU ◽  
X. N. WU
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Critical Point ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Size Analysis ◽  
Honeycomb Lattice ◽  
Correlation Lengths ◽  
Antiferromagnetic Ising Model

In this paper we present highly accurate numerical results of the determination of the critical point of the antiferromagnetic Ising model in a nonzero magnetic field for the honeycomb lattice, including the critical fugacity of a nearest-neighbor exclusion lattice gas. We compute the correlation length of the Ising model using a transfer matrix approach, and locate the critical point from the data on the correlation lengths using finite-size analysis. For the purpose of a maximum numerical accuracy, the analysis is carried out by taking transfer matrices proceeding in two perpendicular directions of the lattice.

WANG–LANDAU SIMULATION ON THERMODYNAMIC AND MAGNETIC PROPERTIES OF HONEYCOMB LATTICE

2011 ◽  
Vol 25 (26) ◽  
pp. 3435-3442
Author(s):  
XIAOYAN YAO
Keyword(s):  
Magnetic Field ◽  
Monte Carlo Simulation ◽  
Magnetic Properties ◽  
Free Energy ◽  
Magnetic Susceptibility ◽  
Magnetic Property ◽  
Ground State ◽  
Antiferromagnetic Order ◽  
Honeycomb Lattice ◽  
Antiferromagnetic Ising Model

Wang–Landau algorithm of Monte Carlo simulation is performed to understand the thermodynamic and magnetic properties of antiferromagnetic Ising model on honeycomb lattice. The internal energy, specific heat, free energy and entropy are calculated to present the thermodynamic behavior. For magnetic property, the magnetization and magnetic susceptibility are discussed at different temperature upon different magnetic field. The antiferromagnetic order is confirmed to be the ground state of the system, and it can be destroyed by a large magnetic field.

GENERAL 8-VERTEX MODEL ON THE HONEYCOMB LATTICE: EQUIVALENCE WITH AN ISING MODEL

1990 ◽  
Vol 04 (05) ◽  
pp. 311-316 ◽  
Author(s):  
K. Y. LIN ◽  
F. Y. WU
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Honeycomb Lattice ◽  
Vertex Model ◽  
Independent Vertex ◽  
Anisotropic Interactions ◽  
Complex Magnetic Field

It is shown that the general 8-vertex model on the honeycomb lattice is always reducible to an Ising model in a nonzero but generally complex magnetic field. In the most general case of the staggered 8-vertex model characterized by 16 independent vertex weights, the equivalent Ising model has three anisotropic interactions and a staggered magnetic field which assumes two different values on the two sublattices.

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.

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