scholarly journals Some Algebraic Techniques for obtaining Low-temperature Series Expansions

1978 ◽  
Vol 31 (6) ◽  
pp. 515 ◽  
Author(s):  
IG Enting
Keyword(s):  
Low Temperature ◽  
Statistical Mechanics ◽  
Series Expansion ◽  
General Result ◽  
Generating Functions ◽  
Finite Lattice ◽  
Lattice Models ◽  
Temperature Series ◽  
Series Expansions ◽  
Lattice Method

It is shown that low-temperature series expansions for lattice models in statistical mechanics can be obtained from a consideration of only connected strong subgraphs of the lattice. This general result is used as the basis of a linked-cluster form of the method of partial generating functions and also as the basis for extending the finite lattice method of series expansion to low-temperature series.

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.

LOW-TEMPERATURE SERIES EXPANSIONS FOR SQUARE-LATTICE ISING MODEL WITH FIRST AND SECOND NEIGHBOUR INTERACTIONS

2002 ◽  
Vol 16 (32) ◽  
pp. 4911-4917
Author(s):  
YEE MOU KAO ◽  
MALL CHEN ◽  
KEH YING LIN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Spontaneous Magnetization ◽  
Temperature Series ◽  
Square Lattice ◽  
Series Expansions ◽  
Zero Field ◽  
Ferromagnetic Ising Model ◽  
Neighbour Interaction

We have calculated the low-temperature series expansions of the spontaneous magnetization and the zero-field susceptibility of the square-lattice ferromagnetic Ising model with first-neighbour interaction J1 and second-neighbour interaction J2 to the 30th and 26th order respectively by computer. Our results extend the previous calculations by Lee and Lin to six more orders. We use the Padé approximants to estimate the critical exponents and the critical temperature for different ratios of R = J2/J1. The estimated critical temperature as a function of R agrees with the estimation by Oitmaa from high-temperature series expansions.

Sign in / Sign up

Export Citation Format

Share Document