We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent yt = 1.58693(9) and the magnetic renormalization exponent yh = 2.48178(5). The corrections to scaling are governed by the irrelevant exponent y1 = −0.821(5).We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent yt = 1.58693(9) and the magnetic renormalization exponent yh = 2.48178(5). The corrections to scaling are governed by the irrelevant exponent y1 = −0.821(5).

arXiv:2603.02962Physica A Statistical Mechanics and its ApplicationsMay 21, 20260 citations

Finite-size scaling of the three-dimensional Ising model

Robert Weston

Physics Letters BOct 1, 199011 citations

Finite-size calculations on the three-dimensional Ising model

Henk W. J. Blöte, G. Kamieniarz

Physica A Statistical Mechanics and its ApplicationsJun 1, 199322 citations

The universality class of 3D site-diluted and bond-diluted Ising systems

Martin Hasenbusch B, Francesco Parisen Toldin, Andrea Pelissetto C +1 more

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behaviour of these systems is affected by slowly decaying scaling corrections which make the accurate determination of their universal asymptotic behaviour quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, ν = 0.683(2), η = 0.036(1), α = −0.049(6), γ = 1.341(4), β = 0.354(1), δ = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, ω = 0.33(3) and ω 2 = 0.82(8).We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behaviour of these systems is affected by slowly decaying scaling corrections which make the accurate determination of their universal asymptotic behaviour quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, ν = 0.683(2), η = 0.036(1), α = −0.049(6), γ = 1.341(4), β = 0.354(1), δ = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, ω = 0.33(3) and ω 2 = 0.82(8).

arXiv:cond-mat/0611707Journal of Statistical Mechanics Theory and ExperimentFeb 21, 200768 citations

Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions

W. Janke, R. Kenna

arXiv:hep-lat/0112037Nuclear Physics B - Proceedings SupplementsMar 1, 20025 citations

Tests of strong scaling in the three-dimensional Ising model

Michael Ellis Fisher, Howard B. Tarko

We study numerically the amplitudes ${E}^{\ifmmode\pm\else\textpm\fi{}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})$ of the ${|\frac{\ensuremath{\Delta}T}{{T}_{c}}|}^{1\ensuremath{-}\ensuremath{\alpha}}$ variation in the spin-spin correlation functions $〈{s}_{\stackrel{\ensuremath{\rightarrow}}{0}}{s}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}}〉$, of three-dimensional Ising models in zero field above and below ${T}_{c}$ . By allowing for reasonable correction terms to the asymptotic behavior ${E}^{\ifmmode\pm\else\textpm\fi{}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})\ensuremath{\approx}{E}_{0}^{\ifmmode\pm\else\textpm\fi{}}{(\frac{R}{a})}^{\ensuremath{\zeta}}$, where $a$ is the lattice spacing, we find consistency with the strong-scaling prediction $\ensuremath{\zeta}=\frac{(1\ensuremath{-}\ensuremath{\alpha})}{\ensuremath{\nu}}\ensuremath{-}d+2\ensuremath{-}\ensuremath{\eta}\ensuremath{\simeq}0.31$, and reasonable agreement with universality and $\ensuremath{\epsilon}$-expansion estimates of the amplitudes ${E}_{0}^{\ifmmode\pm\else\textpm\fi{}}$.We study numerically the amplitudes ${E}^{\ifmmode\pm\else\textpm\fi{}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})$ of the ${|\frac{\ensuremath{\Delta}T}{{T}_{c}}|}^{1\ensuremath{-}\ensuremath{\alpha}}$ variation in the spin-spin correlation functions $〈{s}_{\stackrel{\ensuremath{\rightarrow}}{0}}{s}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}}〉$, of three-dimensional Ising models in zero field above and below ${T}_{c}$. By allowing for reasonable correction terms to the asymptotic behavior ${E}^{\ifmmode\pm\else\textpm\fi{}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})\ensuremath{\approx}{E}_{0}^{\ifmmode\pm\else\textpm\fi{}}{(\frac{R}{a})}^{\ensuremath{\zeta}}$, where $a$ is the lattice spacing, we find consistency with the strong-scaling prediction $\ensuremath{\zeta}=\frac{(1\ensuremath{-}\ensuremath{\alpha})}{\ensuremath{\nu}}\ensuremath{-}d+2\ensuremath{-}\ensuremath{\eta}\ensuremath{\simeq}0.31$, and reasonable agreement with universality and $\ensuremath{\epsilon}$-expansion estimates of the amplitudes ${E}_{0}^{\ifmmode\pm\else\textpm\fi{}}$.

Physical review. B, Solid stateFeb 1, 197517 citations

{T}_{c}

. By allowing for reasonable correction terms to the asymptotic behavior ${E}^{\ifmmode\pm\else\textpm\fi{}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})\ensuremath{\approx}{E}_{0}^{\ifmmode\pm\else\textpm\fi{}}{(\frac{R}{a})}^{\ensuremath{\zeta}}$, where

a

is the lattice spacing, we find consistency with the strong-scaling prediction $\ensuremath{\zeta}=\frac{(1\ensuremath{-}\ensuremath{\alpha})}{\ensuremath{\nu}}\ensuremath{-}d+2\ensuremath{-}\ensuremath{\eta}\ensuremath{\simeq}0.31$, and reasonable agreement with universality and $\ensuremath{\epsilon}$-expansion estimates of the amplitudes ${E}_{0}^{\ifmmode\pm\else\textpm\fi{}}$.