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arXiv:hep-lat/9701007 · Journal of Physics A Mathematical and General

Universal amplitude ratios in the three-dimensional Ising model

Michele Caselle, Martin Hasenbusch B

Published Jul 21, 1997• 74 citations
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Abstract

We present a high precision Monte Carlo study of various universal amplitude ratios of the three-dimensional Ising spin model. Using state of the art simulation techniques we study the model close to criticality in both phases. Great care is taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain , and . Our results are compatible with those obtained by field theoretic methods applied to the theory and high- and low-temperature series expansions of the Ising model. The mismatch with a previous Monte Carlo study by Ruge et al remains to be understood.

DOI
10.1088/0305-4470/30/14/010

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We present a high precision Monte Carlo study of various universal amplitude ratios of the three-dimensional Ising spin model. Using state of the art simulation techniques we study the model close to criticality in both phases. Great care is taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain , and . Our results are compatible with those obtained by field theoretic methods applied to the theory and high- and low-temperature series expansions of the Ising model. The mismatch with a previous Monte Carlo study by Ruge et al remains to be understood.
We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain ${A}_{+}/{A}_{\ensuremath{-}}=0.536(2)$ and ${C}_{+}/{C}_{\ensuremath{-}}=4.713(7)$, where ${A}_{\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{\ifmmode\pm\else\textpm\fi{}}$ are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts +++ and $\ensuremath{-}$ indicate the high- and the low-temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high- and low-temperature series expansions, field theoretic methods, and experiments.
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 review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.
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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.