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.

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.

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.

Transition to long-range order in the three-dimensional random-field Ising model

1991 ◽  
Vol 66 (25) ◽  
pp. 3281-3284 ◽  
Author(s):  
J. P. Hill ◽  
T. R. Thurston ◽  
R. W. Erwin ◽  
M. J. Ramstad ◽  
R. J. Birgeneau
Keyword(s):  
Ising Model ◽  
Random Field ◽  
Long Range ◽  
Three Dimensional ◽  
Range Order ◽  
Long Range Order ◽  
Random Field Ising Model

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.

Sign in / Sign up

Export Citation Format

Share Document