Phase Transitions in Two-Dimensional Spin Systems

1971 ◽  
Vol 49 (10) ◽  
pp. 1327-1334 ◽  
Author(s):  
D. D. Betts ◽  
C. J. Elliott ◽  
R. V. Ditzian
Keyword(s):  
Phase Transition ◽  
Critical Index ◽  
Spin Systems ◽  
Xy Model ◽  
Conformal Transformations ◽  
Long Range Order ◽  
Two Dimensional ◽  
Critical Temperatures ◽  
Temperature Expansion ◽  
High Temperature Expansion

The first nine coefficients have been derived in the exact high temperature expansion of the fluctuation in the long range order in the XY model on the triangular and square lattices. For the triangular lattice seven coefficients have also been obtained in the expansion of the fourth-order fluctuation. The method of conformal transformations has been developed in a form suitable for the analysis of series of this type. Clear evidence is obtained in favor of a phase transition for which the critical index of the fluctuations is γ ≈ 3/2. The critical temperatures kTC/J for the triangular and square lattices are 1.500 ± 0.006 and 0.900 ± 0.006 respectively.

Exact high temperature series expansions for the XY model

1970 ◽  
Vol 48 (13) ◽  
pp. 1566-1577 ◽  
Author(s):  
D. D. Betts ◽  
C. J. Elliott ◽  
M. H. Lee
Keyword(s):  
High Temperature ◽  
Long Range ◽  
Lattice Gas ◽  
Critical Index ◽  
Temperature Series ◽  
Range Order ◽  
Xy Model ◽  
Long Range Order ◽  
Critical Temperatures ◽  
Quantum Lattice Gas

A method is developed for the exact high temperature series expansion of thermodynamic properties of the spin 1/2 XY model of ferromagnetism or of a quantum lattice gas. Eleven coefficients in the specific heat series for the f.c.c. and b.c.c. lattices and nine coefficients in the series for the fluctuation in the long range order for the f.c.c., b.c.c., and s.c. lattices are calculated. From the fluctuation series the critical temperatures Kc−1 ≡ kTc/J are estimated to be 4.520, 2.902, and 2.02 respectively, while the critical index for the square of the fluctuation in the long range order is γ = 1.35.

THE GROUNDSTATES AND PHASES OF THE TWO-DIMENSIONAL FULLY FRUSTRATED XY MODEL

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3939-3950
Author(s):  
PETTER MINNHAGEN ◽  
SEBASTIAN BERNHARDSSON ◽  
BEOM JUN KIM
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Xy Model ◽  
Two Dimensional ◽  
Spin Configuration ◽  
Multicritical Points ◽  
Symmetry Phase

The 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstate of the standard 2D XY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z2-symmetry explained. This means that the class of 2D FFXY models belongs within a U(1) ⊗ Z2 ⊗ Z2-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The implications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FFXY-model.

Finite-size scaling in ferromagnetic spin systems on the pyrochlore lattice

2020 ◽  
pp. 255-266
Author(s):  
K.S. Soldatov ◽  
◽  
M.A. Padalko ◽  
V.S. Strongin ◽  
D.Yu. Kapitan ◽  
...  
Keyword(s):  
Heisenberg Model ◽  
High Performance ◽  
Finite Size ◽  
Spin Systems ◽  
Xy Model ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Cluster Algorithms ◽  
Size Scaling ◽  
Classical Heisenberg Model

In this paper we present the results of the high-performance computations for the Ising model, the XY-model and the classical Heisenberg model for the pyrochlore lattice. We used Wolff and Swendsen-Wang cluster algorithms with GPU parallelization for the calculations. We obtained critical exponents and critical temperatures using finite-size scaling approach.

scholarly journals Comment on ‘Phase transition of a two-dimensional generalized XY model’

2011 ◽  
Vol 44 (20) ◽  
pp. 208001 ◽  
Author(s):  
Aernout C D van Enter ◽  
Silvano Romano ◽  
Valentin A Zagrebnov
Keyword(s):  
Phase Transition ◽  
Xy Model ◽  
Two Dimensional
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