Phase transition and ferrimagnetic long-range order in the mixed-spin Heisenberg model with single-ion anisotropy

2004 ◽  
Vol 70 (10) ◽  
Author(s):  
Guang-Shan Tian ◽  
Hai-Qing Lin
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Heisenberg Model ◽  
Range Order ◽  
Long Range Order ◽  
Mixed Spin

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.

LONG RANGE ORDER IN THE BLUME-EMERY-GRIFFITHS MODEL

1991 ◽  
Vol 05 (23) ◽  
pp. 1583-1590
Author(s):  
M. CORGINI
Keyword(s):  
Phase Transition ◽  
Long Range ◽  
Order Phase Transition ◽  
Range Order ◽  
Long Range Order ◽  
First Order ◽  
First Order Phase Transition ◽  
Infrared Bounds ◽  
First Order Phase

Using the Infrared Bounds method it ws demonstrated that a first order phase transition takes place in the m-dimensional (m≥3) Blume-Emery-Griffiths model.

Study of a model for the main phase transition of lipid bilayers using the Kikuchi cluster method

1984 ◽  
Vol 62 (9) ◽  
pp. 935-942 ◽  
Author(s):  
Alzira M. Stein-Barana ◽  
G. G. Cabrera ◽  
M. J. Zuckermann
Keyword(s):  
Phase Transition ◽  
Lipid Bilayers ◽  
Long Range ◽  
Effective Field ◽  
Order Parameters ◽  
Range Order ◽  
Cluster Method ◽  
Variation Method ◽  
Long Range Order ◽  
Approximate Counting

The statistical mechanics of Doniach's two-state lattice model for the main gel – liquid crystal phase transition of phospholipid bilayers is treated in a similar manner to order–disorder transformations in binary alloys and magnetic systems, using the cluster variation method developed by Kikuchi. Indeed, the analogy holds better for the latter system, since the entropy difference between the two states gives rise to an effective temperature-dependent field. This effective field vanishes at the first-order phase transition, whose latent heat is associated with the discontinuity in the order parameter.We use Kikuchi's approximation with the inclusion of triangle bond correlations, and pair and site probabilities in the expression for free energy. We assume that the lipid chains only interact through nearest neighbour pair potentials and that triangle correlations are important for approximate counting of allowed states. Two long-range order parameters and a short-range order parameter are introduced in the formulation of the theory. Both long-range order parameters are discontinuous at the transition temperature. Numerical results for the physical quantities are presented and discussed with respect to earlier work.

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