Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region

1976 ◽  
Vol 13 (1) ◽  
pp. 316-374 ◽  
Author(s):  
Tai Tsun Wu ◽  
Barry M. McCoy ◽  
Craig A. Tracy ◽  
Eytan Barouch
Keyword(s):  
Ising Model ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Exact Theory ◽  
Scaling Region

scholarly journals n-spin correlation functions for the two-dimensional Ising model

1978 ◽  
Vol 17 (3) ◽  
pp. 1464-1465 ◽  
Author(s):  
John L. Richardson ◽  
Myron Bander
Keyword(s):  
Ising Model ◽  
Correlation Functions ◽  
Spin Correlation ◽  
Two Dimensional

Spin–Spin Correlations in Site Disordered ±J 2D Ising Spin Glasses

1998 ◽  
Vol 09 (05) ◽  
pp. 685-691
Author(s):  
B. Kawecka-Magiera ◽  
A. Z. Maksymowicz ◽  
M. Kowal ◽  
K. Kulakowski
Keyword(s):  
Correlation Functions ◽  
Spin Glasses ◽  
Interatomic Distance ◽  
Spin Correlation ◽  
Two Dimensional ◽  
Spin Correlations ◽  
Ising Spin ◽  
Bond System ◽  
Random Site

Spin–spin correlation functions <S(0)S(R)> as dependent on interatomic distance R are studied in the random-site two-dimensional Ising S=1/2 ±J system. Oscillations of the correlation functions are found, which is not a case in the random-bond system.

Critical indices for spin correlation functions in ferromagnetic films

1979 ◽  
Vol 57 (10) ◽  
pp. 1686-1698 ◽  
Author(s):  
G. Gumbs ◽  
A. Griffin
Keyword(s):  
Correlation Functions ◽  
Finite Thickness ◽  
Mean Field ◽  
Spin Correlation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Critical Indices ◽  
The Mean

Using the Ginzburg–Landau–Wilson (GLW) Hamiltonian, we obtain, with the mean-field approximation, explicit expressions for the spin–spin correlation function χ(z,z′) of a film of thickness L above the phase transition temperature Tc and the spontaneous magnetization [Formula: see text] below Tc. The boundaries are treated using a temperature-independent extrapolation length Λ. From our results, we verify explicitly that for finite L, the critical indices associated with the spin–spin correlation functions and the surface magnetization are identical with those for the analogous two-dimensional system, for both the ordinary (Λ > 0) and surface (Λ < 0) transitions. Our model results nicely exhibit the fact that as long as L is finite, when the temperature T approaches sufficiently close to Tc, there is a crossover from behaviour characteristic of a single surface to two-dimensional behaviour. Within the one-loop, Hartree self-consistent field approximation, we study the effects of mode–mode coupling on the surface layer susceptibility in films of varying thicknesses. The singular behaviour obtained in the mean-field approximation is found to be completely removed in systems of finite thickness, the susceptibilities only exhibiting a finite cusp at the transition.

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