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1 New Estimates On Various Critical/Universal Quantities of the 3D Ising Model ∗

Martin Hasenbusch B, K. Pinn, Universität Münster

Published Jan 1, 1997• 1 citation
OpenAlex

Abstract

We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.

Related papers

A_+/A_-, alpha, nu, and f_s xi^3 from 3D Ising Energy and Specific Heat

Martin Hasenbusch B, K. Pinn

We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite size scaling of the energy E and the specific heat C at criticality we obtain the estimate nu = 0.6308(10). Furthermore, one obtains precise estimates for the ``backgrounds'' (nonsingular parts) E_ns and C_ns. Fitting solely off critical energy estimates to a scaling law, we find depending on the choice of the reduced temperature, either A_+/A_- = 0.550(12) and alpha=0.1115(37), or A_+/A_- = 0.567(16) and alpha=0.1047(48). Including information from the data at T_c, we obtain the estimate A_+/A_- = 0.560(10). We also determine the universal combination f_s xi^3 in both phases.

arXiv:cond-mat/9706003•May 31, 1997•0 citations

, , , and from 3D Ising energy and specific heat

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11 Universal Amplitude Ratios in the Ising Model in Three Dimensions

A. Gordillo-Guerrero, Ralph Kenna B, Juan Jesus Ruiz-Lorenzo +1 more

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A + /A − in the three-dimensional Ising model via the impact angle phgr of complex temperature zeros. We also measure the correlation-length critical exponent ν from finite-size scaling and the specific-heat exponent α through hyperscaling. Extrapolations to the thermodynamic limit yield phgr = 59.2(1.0)°, A + /A − = 0.56(3), ν = 0.630 48(32) and α = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.

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Specific heat of a three dimensional Ising ferromagnet above the Curie temperature. II

M F Sykes, D L Hunter, D S McKenzie +1 more

For pt. I see abstr. A37614 of 1967. High temperature series expansions for the specific heat of the Ising model of a ferromagnet are given for the face-centred cubic, body-centred cubic, and simple cubic lattices. From a numerical study it is concluded that the critical index ( alpha ) is lattice independent and that in three dimensions alpha approximately=1/8. A numerical representation of the specific heat in the range T C <or=T<or= infinity is given in each case, together with estimates of the critical energy, entropy, and free energy. Asymptotic forms for the specific heat and energy are given.

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Energy fluctuations and the singularity of specific heat in a 3D Ising model

J. Kaupužs

We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat Cv based on the finite-size scaling of its maximal values Cvmax depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of Cv. The simulations made up to L ≤ 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of Cvmax in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L ε [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures t ≥ 0.000086 and system sizes L ≤ 410.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•2 citations
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0t**mu, and for the universal combination R_ = sigmaxi2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi3, where fs is the singular part of the free energy.
We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite size scaling of the energy E and the specific heat C at criticality we obtain the estimate nu = 0.6308(10). Furthermore, one obtains precise estimates for the ``backgrounds'' (nonsingular parts) E_ns and C_ns. Fitting solely off critical energy estimates to a scaling law, we find depending on the choice of the reduced temperature, either A_+/A_- = 0.550(12) and alpha=0.1115(37), or A_+/A_- = 0.567(16) and alpha=0.1047(48). Including information from the data at T_c, we obtain the estimate A_+/A_- = 0.560(10). We also determine the universal combination f_s xi^3 in both phases.
We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite-size scaling of the energy E and the specific heat C at criticality we obtain the estimate . Furthermore, one obtains precise estimates for the `backgrounds' (nonsingular parts) and . Fitting solely off-critical energy estimates to a scaling law, we find, depending on the choice of the reduced temperature, either and , or and . Including information from the data at , we obtain the estimate . We also determine the universal combination in both phases.
We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A + / A − in the three-dimensional Ising model via the impact angle ϕ of complex temperature zeros. We also measure the correlation-length critical exponent ν from finite-size scaling and the specific-heat exponent α through hyperscaling. Extrapolations to the thermodynamic limit yield ϕ = 59.2(1.0)°, A + / A − = 0.56(3), ν = 0.630 48(32) and α = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.
We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A + /A − in the three-dimensional Ising model via the impact angle phgr of complex temperature zeros. We also measure the correlation-length critical exponent ν from finite-size scaling and the specific-heat exponent α through hyperscaling. Extrapolations to the thermodynamic limit yield phgr = 59.2(1.0)°, A + /A − = 0.56(3), ν = 0.630 48(32) and α = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.
For pt. I see abstr. A37614 of 1967. High temperature series expansions for the specific heat of the Ising model of a ferromagnet are given for the face-centred cubic, body-centred cubic, and simple cubic lattices. From a numerical study it is concluded that the critical index ( alpha ) is lattice independent and that in three dimensions alpha approximately=1/8. A numerical representation of the specific heat in the range T C <or=T<or= infinity is given in each case, together with estimates of the critical energy, entropy, and free energy. Asymptotic forms for the specific heat and energy are given.
We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat Cv based on the finite-size scaling of its maximal values Cvmax depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of Cv. The simulations made up to L ≤ 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of Cvmax in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L ε [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures t ≥ 0.000086 and system sizes L ≤ 410.