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.

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.

Monte Carlo Simulations of Long Range Order Kinetics in B2 and DO3 Phases

1997 ◽  
Vol 143-147 ◽  
pp. 333-338 ◽  
Author(s):  
E. Kentzinger ◽  
Veronique Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M. Zemirli ◽  
H. Bouzar ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Range Order ◽  
Long Range Order

SPIN-1/2 TWO-DIMENSIONAL ANISOTROPIC HEISENBERG ANTIFERROMAGNETS

1989 ◽  
Vol 03 (09) ◽  
pp. 1435-1441 ◽  
Author(s):  
C.Y. PAN
Keyword(s):  
Renormalization Group ◽  
Long Range ◽  
Ground State ◽  
Two Dimensions ◽  
Range Order ◽  
Group Method ◽  
Long Range Order ◽  
Two Dimensional ◽  
Wide Range ◽  
Heisenberg Antiferromagnets

A real space renormalization group method is applied to study the spin-1/2 two-dimensional anisotropic Heisenberg antiferromagnets. We carry out the calculation on a 5×5 cluster by using a variational approach. The ground-state energy per site is estimated as e0=−0.6845±0.0005 which is in good agreement with other numerical estimates. We also calculate the different ground state energies when anisotropy changes. By comparing with 3×3 cluster calculation the resulting threshold for long range order drops and the curve of the renormalization group parameter vs. anisotropy shows no hint of discontinuity over a wide range of anisotropic parameters. Hence, our calculation suggests that long-range order exists for the ground-state of the spin-1/2 Heisenberg antiferromagnets in two dimensions.

ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES

1993 ◽  
Vol 07 (29n30) ◽  
pp. 1947-1950 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Mean Field ◽  
Range Order ◽  
The Other ◽  
Long Range Order ◽  
Field Phase ◽  
Tree Structures ◽  
Bethe Lattices

We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

scholarly journals Off-Diagonal Long-Range Order in Generalized Hubbard Models

1997 ◽  
Vol 11 (11) ◽  
pp. 1311-1335 ◽  
Author(s):  
Kristel Michielsen ◽  
Hans De Raedt
Keyword(s):  
Density Matrix ◽  
Hubbard Model ◽  
Long Range ◽  
Ground State ◽  
Size Dependence ◽  
State Energy ◽  
System Size ◽  
Range Order ◽  
Long Range Order ◽  
Hubbard Models

We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.

Strongly correlated transition metal oxides

2019 ◽  
Author(s):  
Ελένη Αζά
Keyword(s):  
Dielectric Permittivity ◽  
Single Crystal ◽  
Single Crystals ◽  
Long Range ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Magnetic Order ◽  
Range Order ◽  
Long Range Order ◽  
Strongly Correlated

The discovery of materials with coexisting magnetic and ferroelectric orders, has revived theinterest of condensed matter physics and materials’ science communities maintaining the greatpromise of such fundamental mechanisms in devising applications ranging from portablemagnetoelectric (ME) sensors and memories to radar technologies. The present PhD thesis is a study in the field of strongly correlated systems where coupled properties arise from the interplay of charge and spin degrees of freedom over lattice topologies enabling competing magnetic interactions and therefore emergence of coupling of electric and magnetic order. Non-perovskite, two-dimensional (2D) Na-Mn-O oxides are revisited in scope of this in both polycrystalline and large single crystal forms. Among Na-deficient polymorphs, hexagonal α-Na0.7MnO2 (single crystals) has been investigated for the first time as a playground of competing interactions due to mixed Mnvalence (Mn4+ / Mn3+), fostered by Na vacancies in the structure. The competition of FM (Mn3+-Mn4+) and AFM (Mn3+ -Mn3+) interactions is believed to be the origin of the magnetic instability leading to a glassy ground state leaving also their footprint in the dielectric permittivity measurements. Competing FM and AFΜ interactions are also investigated as the origin of the anisotropic magnetic properties witnessed in a-NaxMnO2 (x= 0.96) single crystals. Neutron single crystal experiments show a well-established AFM long range order which vanishes above 26 K whilea coexistent canted antiferromagnetic state persists up to 45 K. In both alpha powders and aNa0.96MnO2 single crystals, the dielectric permittivity suggests the onset of the commensuratemagnetic long range order (T~ 45 K) which in the case of the powders allows a magnetocapacitance effect. Compositional modulations in β-NaMnO2, which are depicted as an intergrowth of α- and βlike oxygen coordinations, are found to trigger a proper-screw magnetic ground state which evolves into collinear commensurate AFM state. Features in the dielectric permittivity coincide with the onset of the commensurate AFM order giving away also the contribution of the α- structural domains. Further understanding of the mechanisms that dictate the relief of frustrated interactions and establishment of magnetic order together with the role of structural complexity in the form of domains or domain-walls is a direction that warrants further exploration as it will help us to resolve whether other coupled electron degrees of freedom are likely to be generated in this family of oxides.

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.

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