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.

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.

Decimation transformations in high-temperature renormalization-group methods

1987 ◽  
Vol 65 (3) ◽  
pp. 208-213
Author(s):  
N. M. Fujiki ◽  
K. De'Bell
Keyword(s):  
Renormalization Group ◽  
High Temperature ◽  
Square Lattice ◽  
Scaling Relations ◽  
Test Cases ◽  
Nearest Neighbour ◽  
Point Analysis ◽  
Group Methods ◽  
Ising Systems ◽  
Renormalization Group Methods

The high-temperature series renormalization group developed by Betts et al. is modified by using the decimation transformation. A conventional fixed-point analysis of the recursion relations is discussed and, in addition, an analysis based on scaling relations for correlation functions is considered. As test cases, we apply these methods to two-dimensional Ising systems with nearest neighbour interactions. The results for a triangular and a square lattice are presented.

scholarly journals HIGH TEMPERATURE EXPANSION OF STRING FREE ENERGY IN HYPERBOLIC SPACE

1995 ◽  
Vol 10 (22) ◽  
pp. 1619-1626 ◽  
Author(s):  
A.A. BYTSENKO ◽  
S.D. ODINTSOV ◽  
S. ZERBINI
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Normal Modes ◽  
Black Hole Entropy ◽  
Quantum Corrections ◽  
Lower Mass ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Leading Term ◽  
The One

The high temperature behavior of the open bosonic string free energy in the space S1 ⊗ HN with vanishingly small curvature is investigated. The leading term of the high temperature expansion of the one-loop free energy, near the Hagedorn instability, is obtained. The problem of ir regularization of thermodynamical quantities is pointed out. For minimally coupling quantum fields related to the normal modes of strings, the results are similar to the ones valid for Rindler space. In the lower mass string states regime a connection with the quantum corrections to the black hole entropy is outlined.

Padé-approximant study of the phase transition of ortho–para mixtures in solid hydrogen

1987 ◽  
Vol 65 (11) ◽  
pp. 1552-1553
Author(s):  
Hiroshi Miyagi ◽  
Akira Mishima ◽  
Tuto Nakamura
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
High Temperature ◽  
Transition Temperature ◽  
Solid Hydrogen ◽  
Temperature Phase ◽  
Ortho Hydrogen ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Low Temperature Phase

The phase transition of solid hydrogen is studied in the Padé approximation, with newly calculated coefficients in the high-temperature expansion series for the free energy. For the low-temperature phase, the free energy is obtained by a previous libron study of ortho–para mixtures. The transition temperature is predicted to be 2.1Γ for pure ortho-hydrogen. The phase transition disappears at ~ 60% of ortho-hydrogen, in agreement with experiment.

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