ORDERING PROBLEM FOR THE ANTIFERROMAGNETIC POTTS MODEL: T=0 MONTE-CARLO STUDIES

1991 ◽  
Vol 05 (19) ◽  
pp. 3061-3071 ◽  
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH ◽  
A.M. KURBATOV
Keyword(s):  
Monte Carlo ◽  
Long Range ◽  
Potts Model ◽  
Triangular Lattice ◽  
Lattice Models ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order ◽  
Monte Carlo Studies ◽  
Antiferromagnetic Potts Model

AF Potts model MC dynamics at T=0 is considered. It is shown that q=3 square lattice and q=4 triangular lattice models are frozen for local MC algorithm. The nature of the previously discussed long-range order phases is examined and entropically favored states are considered.

LONG-RANGE ORDER FOR THE 3-STATE SQUARE LATTICE POTTS MODEL WITH ANTIFERROMAGNETIC “THE MOVE OF THE KNIGHT” INTERACTIONS

1996 ◽  
Vol 10 (15) ◽  
pp. 731-736
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Potts Model ◽  
Ground State ◽  
Nearest Neighbor ◽  
Two Dimensions ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order

The 3-state square lattice Potts model with interactions of spins belonging to the different sublattices, the nearest-neighbor (NN) interaction and “the move of the knight” (MK) antiferromagnetic interactions which also couples spins on the sublattice A to spins on B, is studied by Monte Carlo simulations. It is shown that the MK-interactions stabilizes the BSS phase in two dimensions, preserving macroscopic degeneracy of the ground state. In a range of competing ferromagnetic (NN) interactions “stripes” or “double-stripes” phases are found.

THE DISAPPEARANCE OF TWO-DIMENSIONAL LONG RANGE ORDER IN THE HEISENBERG MODEL WITH COMPETING INTERACTIONS

1990 ◽  
Vol 04 (15n16) ◽  
pp. 2319-2333 ◽  
Author(s):  
A. F. BARABANOV ◽  
L. A. MAKSIMOV ◽  
O. A. STARYKH
Keyword(s):  
Long Range ◽  
Heisenberg Model ◽  
Spin Correlation ◽  
Range Order ◽  
Square Lattice ◽  
Spin Excitation ◽  
Spin Liquid ◽  
Long Range Order ◽  
Competing Interactions ◽  
Nearest Neighbours

In the frustrated Heisenberg model with first (J1) and second (J2) nearest neighbours interactions on a square lattice the transition from the long range order state (LROS) to spin liquid state (SLS) is found at α = J1/J2 ≅ 0.25. SLS is characterized by the gap in spin excitation spectrum at T = 0 and, hence, by exponential decay of spin correlation function at large distance. As a result, correlation length is temperature independent in SLS in accordance with neutron experiments on doped La 2 CuO 4.

ISING MODEL WITH STRONGLY CORRELATED RANDOM FIELDS

1988 ◽  
Vol 02 (10) ◽  
pp. 1137-1141 ◽  
Author(s):  
T. HORIGUCHI ◽  
L.L. GONCALVES
Keyword(s):  
Ising Model ◽  
Domain Wall ◽  
Long Range ◽  
Random Fields ◽  
Linear Chain ◽  
Ising Models ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order ◽  
Strongly Correlated

We investigate the Ising models with strongly correlated random fields, taking the values ±h0 and 0, on the square lattice and on the linear chain. The models present long range order and these results are consistent with the lower critical dimensionality obtained by the domain wall argument.

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