Zero-temperature properties of quantum spin models on the triangular lattice III: the Heisenberg antiferromagnet

1987 ◽  
Vol 65 (5) ◽  
pp. 489-491 ◽  
Author(s):  
S. Fujiki
Keyword(s):  
Triangular Lattice ◽  
Ground State ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
Spin Models ◽  
Spin Correlations ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] Heisenberg antiferromagnet has been extended to an N = 21 site triangular lattice. The infinite-lattice ground state energy per bond is estimated to be E0/3NJ = −0.3678 ± 0.005 by fitting a quadratic in 1/N to the finite N data. The plaquette chirality order is slightly greater than in the XY antiferromagnet. The two-spin correlation is conjectured to decay as [Formula: see text].

Zero-temperature properties of quantum spin models on a triangular lattice I: the ferromagnet

1986 ◽  
Vol 64 (8) ◽  
pp. 876-881 ◽  
Author(s):  
S. Fujiki ◽  
D. D. Betts
Keyword(s):  
Triangular Lattice ◽  
Ground State ◽  
State Energy ◽  
Quantum Spin ◽  
Nearest Neighbour ◽  
Zero Temperature ◽  
Pair Correlations ◽  
Spin Correlations ◽  
Longitudinal Correlation ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] ferromagnet has been extended to an N = 21 site triangular lattice. By fitting a quadratic in 1/N to the nearest neighbour transverse pair correlations, we have estimated the ground-state energy per bond on the infinite lattice to be E0/3NJ = −0.5326 ± 0.003. We conjecture that the square of the magnetization per site vanishes very sharply as N−0.06. The nearest neighbour longitudinal correlation per bond [Formula: see text] for all two-dimensional lattices.

Zero-temperature properties of quantum spin models on the triangular lattice II: the antiferromagnet

1987 ◽  
Vol 65 (1) ◽  
pp. 76-81 ◽  
Author(s):  
S. Fujiki ◽  
D. D. Betts
Keyword(s):  
Triangular Lattice ◽  
State Energy ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Transverse Spin ◽  
Nearest Neighbour ◽  
Spin Correlations ◽  
Infinite Lattice ◽  
Longitudinal Correlation ◽  
Quantum Spin Models

The calculation of two- and four-spin correlations of the [Formula: see text] antiferromagnet has been extended to an N = 21 site triangular lattice. By fitting a quadratic in 1/N to the nearest neighbour transverse spin correlations, we have estimated the ground-state energy per bond on the infinite lattice to be E0/3NJ = −0.2716 ± 0.005. The nearest neighbour longitudinal correlation is estimated to be [Formula: see text]. A short-range order parameter, the chirality, is defined and estimated for the infinite lattice. From the N dependence of the three sublattice or helical magnetization, the spin correlation is conjectured to decay algebraically as [Formula: see text].

scholarly journals Ground-state properties of linear-exchange quantum spin models

2012 ◽  
Vol 100 (2) ◽  
pp. 27003 ◽  
Author(s):  
Bimla Danu ◽  
Brijesh Kumar ◽  
Ramesh V. Pai
Keyword(s):  
Ground State ◽  
Quantum Spin ◽  
Spin Models ◽  
Ground State Properties ◽  
Quantum Spin Models ◽  
Linear Exchange

scholarly journals Site-Monotonicity Properties for Reflection Positive Measures with Applications to Quantum Spin Systems

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Benjamin Lees ◽  
Lorenzo Taggi
Keyword(s):  
Spin Correlation ◽  
Quantum Spin ◽  
Heisenberg Antiferromagnet ◽  
Quantum Spin Systems ◽  
Point Function ◽  
Dimer Model ◽  
Spin Correlations ◽  
Mechanics Model ◽  
Monotonicity Properties ◽  
General Statistical

AbstractWe consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model and lattice permutations, thus extending the previous results of Lees and Taggi (2019).

Sign in / Sign up

Export Citation Format

Share Document