High-temperature series expansions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>-state Potts model on a hypercubic lattice and critical properties of percolation

Hellmund, Meik; Janke, Wolfhard

doi:10.1103/physreve.74.051113

Cited by 17 publications

(16 citation statements)

References 35 publications

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“…The estimates are correlated and the jackknife procedure takes care of correct error bars. Also it should be noted that β t in the arguments of e, s and f is β 2 t , defined as the extrapolation of the pseudo transition temperatures as defined by (21). These values are consistent with the β t values listed in table IV, but not identical, as β t of table IV is the average of the extrapolations from our three definitions of pseudo transition temperatures.…”

Section: Entropy and Energy Across The Phase Transitionssupporting

confidence: 84%

Phase transition properties of 3D Potts models

2008

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Section: Entropy and Energy Across The Phase Transitionssupporting

confidence: 84%

Phase transition properties of 3D Potts models

2008

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“…Interestingly, the found values are very close to the critical exponent γ of the mean cluster size in standard percolation theory in three dimensions[118][119][120]. Even though the discussion of a possible connection is beyond the scope of the present article, it might be worthwhile to investigate it in the future.…”

supporting

confidence: 67%

Observational prospects for gravitational waves from hidden or dark chiral phase transitions

2019

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We study the gravitational wave (GW) signature of first-order chiral phase transitions (χPTs) in strongly interacting hidden or dark sectors. We do so using several effective models in order to reliably capture the relevant non-perturbative dynamics. This approach allows us to explicitly calculate key quantities characterizing the χPT without having to resort to rough estimates. Most importantly, we find that the transition's inverse duration β normalized to the Hubble parameter H is at least two orders of magnitude larger than typically assumed in comparable scenarios, namely, β/H O(10 4 ). The obtained GW spectra then suggest that signals from hidden χPTs occurring at around 100 MeV might be in reach of LISA, while DECIGO and BBO may detect a stochastic GW background associated with transitions between roughly 1 GeV and 10 TeV. Signatures of transitions at higher temperatures are found to be outside the range of any currently proposed experiment. Even though predictions from different effective models are qualitatively similar, we find that they may vary considerably from a quantitative point of view, which highlights the need for true first-principle calculations such as lattice simulations. CONTENTS

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“…For the remaining two exponents σ and τ, we note that the estimates for τ are in good agreement over all dimensions in comparison with Monte Carlo estimates given in Table I of Ref. [62]. An estimate for σ of around 0.452-0.454 is given there, too, but only in three dimensions.…”

Section: Percolationmentioning

confidence: 52%

“…To compare we have included the results of the computation of ν, γ, η, and β [61] in Table IX which used a high temperature series method. Though, it is worth noting that a more recent study [62] has obtained estimates for γ which are equivalent to the those of the high temperature series of Ref. [61].…”

Section: Percolationmentioning

confidence: 89%

Four loop renormalization ofϕ3theory in six dimensions

2015

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We renormalize six-dimensional ϕ 3 theory in the modified minimal subtraction (MS) scheme at four loops. From the resulting β-function, anomalous dimension, and mass anomalous dimension, we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two-dimensional conformal field theory, we obtain estimates for exponents in dimensions 3, 4, and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an OðNÞ symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this OðNÞ analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigenexponents are in agreement with the mass exponents computed at Oð1=N 2 Þ in the nonperturbative large N expansion.

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High-temperature series expansions for theq-state Potts model on a hypercubic lattice and critical properties of percolation

Cited by 17 publications

References 35 publications

Phase transition properties of 3D Potts models

Phase transition properties of 3D Potts models

Observational prospects for gravitational waves from hidden or dark chiral phase transitions

Four loop renormalization ofϕ3theory in six dimensions

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