The generalization of the Mermin–Wagner theorem and the possibility of long-range order in the isotropic discrete one-dimensional quantum Heisenberg model

2012 ◽  
Vol 324 (21) ◽  
pp. 3605-3609
Author(s):  
Yu.G. Rudoy ◽  
O.A. Kotelnikova
Keyword(s):  
Long Range ◽  
Heisenberg Model ◽  
Range Order ◽  
Long Range Order ◽  
One Dimensional

Non-periodic long-range order for one-dimensional pair interactions

1997 ◽  
Vol 30 (2) ◽  
pp. 501-505 ◽  
Author(s):  
Aernout C D van Enter ◽  
Boguslaw Zegarlinski
Keyword(s):  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
One Dimensional ◽  
Pair Interactions

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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