Field theory of the two-dimensional ising model: II. Nonlocal specific heat

1981 ◽  
Vol 25 (2) ◽  
pp. 361-366
Author(s):  
Richard A. Ferrell
Keyword(s):  
Field Theory ◽  
Ising Model ◽  
Specific Heat ◽  
Two Dimensional

KNOTTED VORTICES AND SUPERFLUID PHASE TRANSITION

1993 ◽  
Vol 07 (23) ◽  
pp. 1523-1526 ◽  
Author(s):  
ROBERT OWCZAREK
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Specific Heat ◽  
Superfluid Helium ◽  
Vortex Structures ◽  
Two Dimensional ◽  
Superfluid Phase ◽  
Λ Point

In this letter, studies of knotted vortex structures in superfluid helium are continued. A model of superfluid phase transition (λ-transition) is built in this framework. Similarities of this model to the two-dimensional Ising model are shown. Dependence of specific heat of superfluid helium on temperature near the λ point is explained.

Quantum field theory and the two-dimensional Ising model

1977 ◽  
Vol 15 (10) ◽  
pp. 2875-2884 ◽  
Author(s):  
J. B. Zuber ◽  
C. Itzykson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ising Model ◽  
Quantum Field ◽  
Two Dimensional

The Finite-Size Scaling Study of the Specific Heat and the Binder Parameter of the Two-Dimensional Ising Model for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

2009 ◽  
Vol 64 (12) ◽  
pp. 849-854 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Straight Line ◽  
Binder Parameter

The two-dimensional Ising model with nearest-neighbour pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 80, 120, 160, and 200. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice Tc = 2.287(6), Tc = 2.269(3), and Tc =2.271(1) are obtained from the intersection points of specific heat curves, Binder parameter curves, and the straight line fit of specific heat maxima, respectively. These results are in agreement with the theoretical value (Tc =2.269) within the error limits. The values obtained for the critical exponent of the specific heat, α = 0.04(25) and α = 0.03(1), are in agreement with α = 0 predicted by the theory. The values for the Binder parameter by using the finite-size lattices with the linear dimension L = 80, 120, 160, and 200 at Tc = 2.269(3) are calculated as gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2), respectively. The value of the infinite lattice for the Binder parameter, gL(Tc) = −1.834(11), is obtained from the straight line fit of gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2) versus L = 80, 120, 160, and 200, respectively

Critical Phenomena at the Antiferromagnetic Transition in MnO

1999 ◽  
Vol 602 ◽  
Author(s):  
B.F. Woodfield ◽  
J.L. Shapiro ◽  
R. Stevens ◽  
J. Boerio-Goates ◽  
M.L. Wilson
Keyword(s):  
Ising Model ◽  
Critical Exponent ◽  
Specific Heat ◽  
Temperature Dependence ◽  
Low Temperatures ◽  
Applied Pressure ◽  
Polycrystalline Sample ◽  
Type Ii ◽  
Two Dimensional ◽  
Antiferromagnetic Transition

AbstractThe specific heat of a polycrystalline sample of MnO was measured from T ≈ 1 K to T ≈ 400 K using two different experimental apparatuses at zero applied pressure. Features revealed by the data include a hyperfine contribution due to the Mn nuclei, a T2 temperature dependence at low temperatures due to the type-II antiferromagnetic magnon contribution, and a sharp but well defined antiferromagnetic transition (TN = 117.7095 K) that is clearly second order in nature. The critical exponent, α, deduced from the transition is consistent with a two dimensional Ising model. The specific heat of MnO is also compared with recent results on the type-A antiferromagnet LaMnO3.

Statistical mechanics of the two-dimensional assembly

1950 ◽  
Vol 202 (1069) ◽  
pp. 202-207 ◽  
Keyword(s):  
Ising Model ◽  
Curie Temperature ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Considerable Effect ◽  
Square Lattice ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Triangular Lattices

The work of Kaufman & Onsager (1946) on the two-dimensional Ising model of a ferromagnet is extended from the plane square lattice to the plane honeycomb and triangular lattices. The specific heat anomaly, where it exists, turns out to be of the same type in all three lattices, an infinity in the specific heat at the Curie temperature. It is concluded that second-nearest neighbour interactions may have a considerable effect on the position of the Curie temperature.

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