aqora

Delta expansion at low temperatures

Yamada, Hirofumi

In the low temperature phase of the square Ising model, we describe the inverse temperature beta as the function of a squared mass M and study the critical behavior of beta(M) via the large M expansion. Using the delta-expansion by which the large mass expansion is transformed into a series exhibiting expected scaling behavior, we perform the estimation of the critical inverse temperature beta_{c} with the help of linear differential equation to be satisfied by ansatz of beta(M) near the critical point M=0. To improve the estimation, the leading correction exponent nu is independently estimated from beta^{(2)}/beta^{(1)} and is used in the estimation of beta_{c}, giving rise to remarkable accuracy improvement.In the low temperature phase of the square Ising model, we describe the inverse temperature beta as the function of a squared mass M and study the critical behavior of beta(M) via the large M expansion. Using the delta-expansion by which the large mass expansion is transformed into a series exhibiting expected scaling behavior, we perform the estimation of the critical inverse temperature beta_{c} with the help of linear differential equation to be satisfied by ansatz of beta(M) near the critical point M=0. To improve the estimation, the leading correction exponent nu is independently estimated from beta^{(2)}/beta^{(1)} and is used in the estimation of beta_{c}, giving rise to remarkable accuracy improvement.

arXiv:1410.5751Oct 21, 20140 citations

On the critical dynamics of one-dimensional Ising models

Michel Droz, J. Kamphorst Leal da Silva, Anna‐Sapfo Malaspinas

Physics Letters AMay 1, 198649 citations

Determination of critical behaviour from series expansions in lattice statistics. IV

Anthony John Guttmann, Colin J. Thompson, Barry William Ninham

For pt. III, see abstr. A21890 of 1970. A new low-temperature expansion variable for the Ising model is given. Expansions in the new variable, x=1-tanh(J/kT), then converge right up to the critical point. Power series in the new variable are derived, and then analysed by the Pade method and the method of N-point fits. For the spontaneous magnetization of the Ising model in three dimensions. beta =0.312+or-0.002 for the simple cubic lattice, beta =0.3125+or-0.0015 for the body-centred cubic lattice, and beta =0.312+or-0.004 for the face-centred cubic lattice. For the low-temperature susceptibility gamma =1.30+or-0.02, gamma =1.28+or-0.04, and gamma '=1.29+or-0.04 for the simple cubic, body-centred cubic and face-centred cubic lattices respectively. For the low-temperature specific heat the authors estimate 1 / 16 <or= alpha =0.2 for all three lattices.For pt. III, see abstr. A21890 of 1970. A new low-temperature expansion variable for the Ising model is given. Expansions in the new variable, x=1-tanh(J/kT), then converge right up to the critical point. Power series in the new variable are derived, and then analysed by the Pade method and the method of N-point fits. For the spontaneous magnetization of the Ising model in three dimensions. beta =0.312+or-0.002 for the simple cubic lattice, beta =0.3125+or-0.0015 for the body-centred cubic lattice, and beta =0.312+or-0.004 for the face-centred cubic lattice. For the low-temperature susceptibility gamma =1.30+or-0.02, gamma =1.28+or-0.04, and gamma '=1.29+or-0.04 for the simple cubic, body-centred cubic and face-centred cubic lattices respectively. For the low-temperature specific heat the authors estimate 1 / 16 <or= alpha =0.2 for all three lattices.

Journal of Physics C Solid State PhysicsAug 1, 197014 citations

On the series expansion of the general spin-S Ising chain

Onofre Rojas, S. M. de Souza, W. A. Moura-Melo

Physica A Statistical Mechanics and its ApplicationsJul 8, 20064 citations

Two analytic approximations for thed+1 ising model

Cayetano Di Bartolo, Lorenzo Leal

Il Nuovo Cimento DAug 1, 19910 citations

Estimation of critical indices for the three-dimensional Ising model

David S. Gaunt, M F Sykes

New series expansion data for the three-dimensional Ising model are analysed. A special study of the diamond and face-centred cubic lattices is made. Below the critical temperature convergence is found to be slow. It is concluded that all available data are consistent with beta = lambda 5/16 (magnetization) and not inconsistent with the 'scaling' value gamma '=5/4 (susceptibility) and that with the data and methods available at present it is not possible to draw more precise conclusions.New series expansion data for the three-dimensional Ising model are analysed. A special study of the diamond and face-centred cubic lattices is made. Below the critical temperature convergence is found to be slow. It is concluded that all available data are consistent with beta = lambda 5/16 (magnetization) and not inconsistent with the 'scaling' value gamma '=5/4 (susceptibility) and that with the data and methods available at present it is not possible to draw more precise conclusions.

Journal of Physics A Mathematical Nuclear and GeneralOct 1, 197349 citations

Remarks on the convergence of the β-expansion of and s=1 Ising models

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