Ising Model with a Long-Range Interaction in the Presence of Residual Short-Range Interactions

1963 ◽  
Vol 130 (4) ◽  
pp. 1406-1411 ◽  
Author(s):  
George A. Baker
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Short Range ◽  
Range Interaction ◽  
Long Range Interaction

One-dimensional Ising model with long-range interaction

1970 ◽  
Vol 31 (9) ◽  
pp. 479-480 ◽  
Author(s):  
L.J. Kijewski ◽  
M.P. Kawatra
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Range Interaction ◽  
One Dimensional ◽  
Long Range Interaction

On the Ising Model with Long‐Range Interaction

1968 ◽  
Vol 9 (12) ◽  
pp. 2173-2193 ◽  
Author(s):  
A. J. F. Siegert ◽  
David J. Vezzetti
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Range Interaction ◽  
Long Range Interaction

scholarly journals Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete

2019 ◽  
pp. 37-47 ◽  
Author(s):  
S.V. Belim
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Exponents ◽  
Short Range ◽  
Asymptotic Series ◽  
Critical Behaviour ◽  
Interaction Parameters ◽  
Theory Approach ◽  
Range Interaction ◽  
Long Range Interaction

Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a distinctive critical behaviour mode for these values. We derived vertex functions using a two-loop approximation directly in three-dimensional space (D = 3) and, for all values, obtained a linear approximation of asymptotic series in terms of long-range interaction parameters. We applied the Pade --- Borel summation technique to these asymptotic series. We computed stable fixed points and critical exponents as functions of long-range interaction parameters for low relativeefficiency of the long-range interaction. We investigated how critical exponents depend on the factor in the power law and relative long-range interaction intensity. We compared our results to the critical exponent values found experimentally for manganites. We used the experimental critical exponent γ values to compute long-range interaction parameters and then used the long-range interaction parameters to derive the ß exponent values, which we then compared to the experimental values. We show good agreement between our theoretical results and experimental data.

scholarly journals Long-range vector models at large N

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Noam Chai ◽  
Mikhail Goykhman ◽  
Ritam Sinha
Keyword(s):  
Long Range ◽  
Short Range ◽  
Conformal Symmetry ◽  
Vector Model ◽  
Entire Region ◽  
Crossover Point ◽  
Range Interaction ◽  
Large N ◽  
Long Range Interaction ◽  
Range Vector

Abstract We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s* of the exponent parameter s. We also develop the N > 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 < s < s*.

scholarly journals Time-Dependent Ising Model with Long Range Interaction

1968 ◽  
Vol 39 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Kyozi Kawasaki ◽  
Tomoji Yamada
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Time Dependent ◽  
Range Interaction ◽  
Long Range Interaction
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