Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0202017 · Journal of Physics A Mathematical and General

Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

Attilio Cucchieri A, J Engels, S Holtmann, T Mendes, T Schulze

Published Jul 25, 2002• 28 citations
arXivHTMLPDF

Abstract

We investigate the three-dimensional O(2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U_0=A+/A- is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow to extract an accurate estimate for alpha. Instead, we establish a strong correlation of U_0 with the value of alpha used in the fit. This numerical alpha-dependence is given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values used in other calculations we find full agreement with the corresponding ratio values, e. g. that of the shuttle experiment with liquid helium. On the critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the used alpha or nu-values.

DOI
10.1088/0305-4470/35/31/301

Related papers

Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

Attilio Cucchieri A, Engels, Jürgen, Sven Holtmann +2 more

We investigate the three-dimensional 0 (2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U-0 = A(+)/A(-) is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow us to extract an accurate estimate for a. Instead, we establish a strong correlation of U0 with the value of a used in the fit. This numerical a-dependence is given by A(+)/A(-) = 1 - 4.20(5)alpha + O(alpha(2)). For the special alpha-values used in other calculations, we find full agreement with the corresponding ratio values, e.g. that of the shuttle experiment with liquid helium. On the critical isochore, we obtain the ratio 0.293(9), and on the critical line the ratio xi(T)(C) / xi(L)(C) = 1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the alpha- or v-values used here.

•Jan 1, 2002•28 citations

Universal amplitude ratios in the Ising model in three dimensions

A Gordillo-Guerrero, R Kenna, J J Ruiz-Lorenzo

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.

arXiv:1107.1186•Journal of Statistical Mechanics Theory and Experiment•Sep 20, 2011•4 citations

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.

•Jan 1, 2011•7 citations

External field dependence of the correlation lengths in the three-dimensional O(4) model

J. Engels, Lars Fromme, Michael Seniuch

We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of the transverse correlation length, which is expected due to the Goldstone modes of the model. On the critical line we find the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1). From our data we derive the universal scaling function for the transverse correlation length. The H-dependencies of the correlation lengths in the high temperature phase are discussed and shown to be in accord with the scaling functions.

•Jan 1, 2003•1 citation

High-precision determination of universal amplitude ratios for the q=3 Potts model in two dimensions

Щур Лев Николаевич, Bertrand Berche, P. Butera

Monte Carlo simulations and series expansions data for the energy, specific heat, magnetization, and susceptibility of the three-state Potts model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We estimate these amplitudes using the correction-to-scaling exponents predicted by conformal field theory. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\ensuremath{\leqslant}4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. We present numerical and analytical support for the form of the first two correction-to-scaling terms. Our results for the amplitude ratios closely agree with the theoretical predictions and the earlier numerical estimates of the specific heat and the susceptibility amplitude ratios.

arXiv:0801.2719•Physical Review B•Apr 9, 2008•14 citations

Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model

Щур Лев Николаевич, Bertrand Berche, P. Butera

Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. The RG predictions on the cancelation of the logarithmic corrections in the universal amplitude ratios are tested. A direct calculation of the effective ratio of the energy amplitudes using duality relations explicitly demonstrates this cancelation of logarithms, thus supporting the predictions of RG. We emphasize the role of corrections and of background terms on the determination of the amplitudes. The ratios of the critical amplitudes of the susceptibilities obtained in our analysis differ significantly from those predicted theoretically and supported by earlier SE and MC analysis. This disagreement might signal that the two-kink approximation used in the analytical estimates is not sufficient to describe with fair accuracy the amplitudes of the 4-state model.

arXiv:0809.4553•Nuclear Physics B•Dec 2, 2008•18 citations
We investigate the three-dimensional O(2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U_0=A+/A- is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow to extract an accurate estimate for alpha. Instead, we establish a strong correlation of U_0 with the value of alpha used in the fit. This numerical alpha-dependence is given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values used in other calculations we find full agreement with the corresponding ratio values, e. g. that of the shuttle experiment with liquid helium. On the critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the used alpha or nu-values.
We investigate the three-dimensional 0 (2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U-0 = A(+)/A(-) is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow us to extract an accurate estimate for a. Instead, we establish a strong correlation of U0 with the value of a used in the fit. This numerical a-dependence is given by A(+)/A(-) = 1 - 4.20(5)alpha + O(alpha(2)). For the special alpha-values used in other calculations, we find full agreement with the corresponding ratio values, e.g. that of the shuttle experiment with liquid helium. On the critical isochore, we obtain the ratio 0.293(9), and on the critical line the ratio xi(T)(C) / xi(L)(C) = 1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the alpha- or v-values used here.
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.
We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of the transverse correlation length, which is expected due to the Goldstone modes of the model. On the critical line we find the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1). From our data we derive the universal scaling function for the transverse correlation length. The H-dependencies of the correlation lengths in the high temperature phase are discussed and shown to be in accord with the scaling functions.
Monte Carlo simulations and series expansions data for the energy, specific heat, magnetization, and susceptibility of the three-state Potts model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We estimate these amplitudes using the correction-to-scaling exponents predicted by conformal field theory. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\ensuremath{\leqslant}4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. We present numerical and analytical support for the form of the first two correction-to-scaling terms. Our results for the amplitude ratios closely agree with the theoretical predictions and the earlier numerical estimates of the specific heat and the susceptibility amplitude ratios.
Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. The RG predictions on the cancelation of the logarithmic corrections in the universal amplitude ratios are tested. A direct calculation of the effective ratio of the energy amplitudes using duality relations explicitly demonstrates this cancelation of logarithms, thus supporting the predictions of RG. We emphasize the role of corrections and of background terms on the determination of the amplitudes. The ratios of the critical amplitudes of the susceptibilities obtained in our analysis differ significantly from those predicted theoretically and supported by earlier SE and MC analysis. This disagreement might signal that the two-kink approximation used in the analytical estimates is not sufficient to describe with fair accuracy the amplitudes of the 4-state model.