scholarly journals High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

2007 ◽  
Vol 118 (5) ◽  
pp. 855-864 ◽  
Author(s):  
H. Arisue
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Xy Model ◽  
Two Dimensional ◽  
Temperature Expansion ◽  
High Temperature Expansion

HIGH-TEMPERATURE SERIES FOR THERMODYNAMIC FUNCTIONS

2003 ◽  
Vol 02 (01) ◽  
pp. 1-5 ◽  
Author(s):  
FRANCISCO M. FERNÁNDEZ
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
High Temperature ◽  
Thermodynamic Functions ◽  
Temperature Series ◽  
Present Approach ◽  
Rigid Rotor ◽  
Temperature Expansion ◽  
High Temperature Expansion

We propose a high-temperature expansion for thermodynamic functions. As an example we calculate the free energy for a restricted plane rigid rotor and compare present approach with perturbation theory.

Dynamical Properties of the Three-Dimensional XY Model. II. Singularity Structure of the Frequency Dependent Susceptibility

1972 ◽  
Vol 50 (20) ◽  
pp. 2415-2420 ◽  
Author(s):  
S. R. Mattingly ◽  
D. D. Betts
Keyword(s):  
High Temperature ◽  
High Frequency ◽  
Three Dimensional ◽  
Xy Model ◽  
Temperature Expansion ◽  
Singularity Structure ◽  
Strong Singularity ◽  
High Temperature Expansion ◽  
Dynamical Properties ◽  
Frequency Temperature

Twenty coefficients are presented in the exact high frequency, high temperature expansion of the perpendicular susceptibility of the spin-1/2 XY model on the f.c.c. lattice. Padé approximant analysis reveals a weak high frequency, temperature independent singularity at ω ≈ (14 ± 2)J/h which we identify with a "quasi-atomic" resonance at ω = 12J/h. We also find a strong singularity at a lower frequency which decreases with decreasing temperature, and for which we have not yet found a satisfying explanation.

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.

High temperature multigraph expansions for general Ising systems

1981 ◽  
Vol 59 (1) ◽  
pp. 15-21 ◽  
Author(s):  
J. Oitmaa
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Square Lattice ◽  
Zero Field ◽  
Nearest Neighbour ◽  
Temperature Expansion ◽  
Graphical Information ◽  
Ising Systems ◽  
High Temperature Expansion ◽  
Multiple Edges

A high temperature expansion, in terms of connected graphs with single and multiple edges, is developed for general Ising systems with interactions of more than one type. The graphical information obtained is sufficient to derive 11 terms in the expansion of the high temperature zero-field susceptibility and 12 terms in the zero-field free energy for any Ising system. Series to this order are presented for the square lattice with nearest and next nearest neighbour interactions.

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