Monte Carlo simulation of the easy‐axis antiferromagnetic Heisenberg model on a stacked triangular lattice

1990 ◽  
Vol 67 (9) ◽  
pp. 5418-5420 ◽  
Author(s):  
A. Mailhot ◽  
M. L. Plumer ◽  
A. Caillé
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Easy Axis ◽  
Antiferromagnetic Heisenberg Model

MONTE CARLO SIMULATION OF A 3-D FRUSTRATED HEISENBERG MODEL

1993 ◽  
Vol 04 (06) ◽  
pp. 1161-1165
Author(s):  
ALAIN BILLOIRE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Antiferromagnetic Heisenberg Model

I present simulations of the classical antiferromagnetic Heisenberg model on a 3-D stacked triangular lattice. The program simulates three independent systems, one third of each system being updated in parallel. It performs between 600 and 800 MegaFlops on a 32 nodes CM-5.

Phase Transitions in the Antiferromagnetic Heisenberg Model on a Triangular Lattice with the Next-Nearest Neighbor Interactions

2014 ◽  
Vol 215 ◽  
pp. 3-10
Author(s):  
Akai K. Murtazaev ◽  
Magomedsheykh K. Ramazanov
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Behavior ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Histogram Method ◽  
First Order Phase Transition ◽  
Antiferromagnetic Heisenberg Model

The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.

EFFECTIVE MEAN-FIELD THEORY BASED ON CUMULANT EXPANSION IN TREATING CLASSICAL HEISENBERG MODEL ON STACKED TRIANGULAR LATTICE

2011 ◽  
Vol 25 (06) ◽  
pp. 833-841
Author(s):  
LIMIN YANG ◽  
SONGQING ZHAO ◽  
KUN ZHAO ◽  
YUNXIA FAN ◽  
P. LI ◽  
...  
Keyword(s):  
Field Theory ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Spin System ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Cumulant Expansion ◽  
The Third

An effective mean-field theory based on cumulant expansion was used to deal with antiferromagnetic Heisenberg model on planar triangular lattice. The corrections of expansion were performed to the third order. By using the equation of the mean field condition, curves of internal energy E specific heat C staggered helicity K (order parameter) and the variational ratio of staggered helicity X were obtained when the proper values of effective external field were achieved. The calculated results showed that there were two phases (which were ordered antiferromagnetic phase and the disordered phase) in the spin system. The first order critical point is -kTc/Js = 1.65, the second is -kTc/Js = 1.35 and the third is -kTc/Js = 1.29, obviously closer to that of Monte Carlo simulation order by order. And also, the analytic expansion curves derived from this method exhibited higher proximity order by order to the Monte Carlo simulation. Such results showed that this method was a useful tool to obtain thermodynamically observables of spin system.

scholarly journals Critical behavior of the antiferromagnetic Heisenberg model on a stacked triangular lattice

1994 ◽  
Vol 4 (2) ◽  
pp. 181-186 ◽  
Author(s):  
T. Bhattacharya ◽  
A. Billoire ◽  
R. Lacaze ◽  
Th. Jolicoeur
Keyword(s):  
Critical Behavior ◽  
Triangular Lattice ◽  
Heisenberg Model ◽  
Antiferromagnetic Heisenberg Model
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