High-temperature properties of the Ising model on the cristobalite lattice

1968 ◽  
Vol 46 (8) ◽  
pp. 971-975 ◽  
Author(s):  
D. D. Betts ◽  
R. V. Ditzian
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Curie Temperature ◽  
Coordination Number ◽  
Critical Energy ◽  
Critical Parameters ◽  
High Temperature Properties ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Effect Of Structure

The high-temperature properties of the Ising model on the cristobalite lattice are investigated by series expansion methods. The Curie temperature is found to be vl = tanh J/kTl = 0.2330 ± 0.003, the amplitude of the singularity in the susceptibility is Γ = 1.100 ± 0.001, the critical energy is −Ec/kTc = 0.268 ± 0.006, and the critical entropy is Sc/k = 0.548 ± 0.003. A comparison of critical parameters for the cristobalite and simple cubic lattices allows one to see the effect of structure for two lattices of the same coordination number.

High-temperature properties of the Ising model on the octahedral lattice

1970 ◽  
Vol 48 (20) ◽  
pp. 2383-2390 ◽  
Author(s):  
J. Oitmaa ◽  
C. J. Elliott
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Reliable Estimate ◽  
Series Expansions ◽  
High Temperature Properties ◽  
Initial Susceptibility

The high-temperature initial susceptibility and specific heat of the spin 1/2 Ising model on the octahedral lattice are investigated by the method of exact series expansions. From the susceptibility series the critical temperature is found to be νc = tanh J/kTc = 0.1613 ± 0.0001. By using a method due to Gibberd the specific-heat series is calculated to 15 terms but a reliable estimate of the exponent a is not obtained, although the results do support the presently believed value α = 1/8.

scholarly journals High-temperature Thermodynamics of the Hubbard Model

1993 ◽  
Vol 46 (5) ◽  
pp. 613
Author(s):  
J Oitmaa ◽  
JA Henderson
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
Specific Heat ◽  
High Temperatures ◽  
Padé Approximants ◽  
Numerical Results ◽  
Strongly Correlated ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Atomic Limit

Recently derived 10th-order high-temperature expansions for the Hubbard model are used to obtain the ferromagnetic susceptibility and specific heat at high temperatures. Numerical results are obtained for the simple cubic and face-centred cubic lattices by using Pade approximants to sum the series. The results are compared with two solvable limiting cases, namely the non-interacting limit U = 0 and the strongly-correlated or atomic limit t = O.

The spin XY model. V. Moments of the spin–spin correlations in three dimensions

1980 ◽  
Vol 58 (11) ◽  
pp. 1651-1657 ◽  
Author(s):  
D. D. Betts ◽  
E. W. Grundke
Keyword(s):  
High Temperature ◽  
Three Dimensions ◽  
Transverse Spin ◽  
Xy Model ◽  
Spin Correlations ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Text Model ◽  
Critical Amplitudes

Ninth degree high temperature expansions have been obtained for all transverse spin–spin correlations of the [Formula: see text] model on the simple cubic and body centred cubic lattices. Analysis of the series for the second and fourth moments of the correlations yields the estimate of v = 0.689 ± 0.010 and estimates of critical amplitudes. No evidence for violation of hyperscaling is found.

High and Low Temperature Series Estimates for the Critical Temperature of the 3D Ising Model

1998 ◽  
Vol 09 (01) ◽  
pp. 195-209 ◽  
Author(s):  
Zaher Salman ◽  
Joan Adler
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Low Temperature ◽  
Three Dimensional ◽  
Temperature Series ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Error Bars ◽  
Temperature Side ◽  
3D Ising Model

We have analyzed low and high temperature series expansions for the three-dimensional Ising model on the simple cubic lattice. Our analysis of Butera and Comi's new 21-term high temperature series yields [Formula: see text] and from the 32-term low temperature series of Vohwinkel we find Kc=0.22167±0.00002, consistent with the high temperature series but with larger error bars. We discuss the reasons for the larger error bars on the low temperature side and compare these values with estimates from other series analyses and from simulations.

scholarly journals CRITICAL EXPONENTS OF THE 3-D ISING MODEL

1996 ◽  
Vol 07 (03) ◽  
pp. 305-319 ◽  
Author(s):  
Rajan Gupta ◽  
Pablo Tamayo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Status Report ◽  
Scaling Exponent ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Correction To Scaling ◽  
Monte Carlo Renormalization Group ◽  
3D Ising Model

We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are [Formula: see text] and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

High-temperature critical properties of the Ising model on a triple of related lattices

1969 ◽  
Vol 47 (16) ◽  
pp. 1671-1689 ◽  
Author(s):  
J. A. Leu ◽  
D. D. Betts ◽  
C. J. Elliott
Keyword(s):  
High Temperature ◽  
Three Dimensional ◽  
Critical Energy ◽  
Temperature Series ◽  
Critical Parameters ◽  
Series Expansions ◽  
Critical Properties ◽  
Coordination Numbers ◽  
Exact Relations ◽  
Temperature Susceptibility

Three regular three-dimensional lattices of coordination numbers, q = 3, 4, and 6 are introduced. Exact relations are derived among the specific-heat singularity amplitudes and among the susceptibility singularity amplitudes. Exact high-temperature series expansions for the partition function and the susceptibility are derived for the q = 3 and q = 6 lattices. Precise values of the critical temperature, susceptibility amplitude, critical energy, and critical entropy are obtained for all three lattices. The variation of Ising critical parameters with coordination number is discussed.

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