New method for calculating series expansions of correlation functions in thed=2Ising model

1984 ◽  
Vol 30 (1) ◽  
pp. 19-23 ◽  
Author(s):  
Ranjan K. Ghosh ◽  
Robert E. Shrock
Keyword(s):  
Correlation Functions ◽  
New Method ◽  
Series Expansions

scholarly journals A Method for the Generation of Various Ghost Correction Algorithms—the Example of the Positivity Method and the Exponential Method

1991 ◽  
Vol 13 (4) ◽  
pp. 199-212 ◽  
Author(s):  
P. Van Houtte
Keyword(s):  
Pole Figure ◽  
Taylor Series ◽  
The Other ◽  
New Method ◽  
Series Expansions ◽  
Theoretical Scheme ◽  
Taylor Series Expansions ◽  
Exponential Method ◽  
Pole Figure Data

A theoretical strategy is presented that can derive the algorithms of several existing ghost correction methods. The examples of the positivity method and the “GHOST” method are elaborated. A new method is derived as well: the “exponential” method. It can successfully replace the quadratic method as a method that yields an exactly non-negative complete C.O.D.F. from pole figure data. The theoretical scheme that can generate all these algorithms makes use of the fact, that several parameter sets can be defined in order to describe a C.O.D.F. The parameters of one set are then functions of those of the other. The algorithms are derived from Taylor series expansions of these functions.

Static and dynamic real-space renormalization through series expansions for correlation functions

1985 ◽  
Vol 32 (11) ◽  
pp. 7333-7355 ◽  
Author(s):  
J. O. Indekeu ◽  
A. L. Stella ◽  
J. Rogiers
Keyword(s):  
Correlation Functions ◽  
Real Space ◽  
Series Expansions

scholarly journals SOME EXACT FORMULAE ON LONG-RANGE CORRELATION FUNCTIONS OF THE RECTANGULAR ISING LATTICE

2004 ◽  
Vol 18 (02) ◽  
pp. 275-287 ◽  
Author(s):  
SHU-CHIUAN CHANG ◽  
MASUO SUZUKI
Keyword(s):  
Correlation Function ◽  
Low Temperature ◽  
Long Range ◽  
Correlation Functions ◽  
Temperature Series ◽  
Series Expansions ◽  
Free Boundaries ◽  
Ising Lattice ◽  
Range Correlation ◽  
Exact Correlation Functions

We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin–spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this m th row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.

New method of computing correlation functions. I

1977 ◽  
Vol 20 (10) ◽  
pp. 1344-1346
Author(s):  
R. R. Nigmatullin
Keyword(s):  
Correlation Functions ◽  
New Method ◽  
Computing Correlation
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