Field-theoretic calculation of the universal amplitude ratio of correlation lengths in 3D Ising systems

Münster, Gernot; Heitger, Jochen

doi:10.1016/0550-3213(94)90409-x

Cited by 25 publications

(33 citation statements)

References 16 publications

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“…as in Ref. [18], whose critical value is precisely known from Monte Carlo simulations [13] u R = 14. This result is compatible with the assumption of weak binding energy that underlies the Bethe-Salpeter formalism, and is in a very good agreement with the numerical result,…”

Section: Comparison With Numerical Resultsmentioning

confidence: 99%

Bound states and glueballs in three-dimensional Ising systems

et al. 2002

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We study the spectrum of massive excitations in three-dimensional models belonging to the Ising universality class. By solving the BetheSalpeter equation for 3D φ 4 theory in the broken symmetry phase we show that recently found non-perturbative states can be interpreted as bound states of the fundamental excitation. We show that duality predicts an exact correspondence between the spectra of the Ising model in the broken symmetry phase and of the Z 2 gauge theory in the confining phase. The interpretation of the glueball states of the gauge theory as bound states of the dual spin system allows us to explain the qualitative features of the glueball spectrum, in particular, its peculiar angular momentum dependence.

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Section: Comparison With Numerical Resultsmentioning

confidence: 99%

Bound states and glueballs in three-dimensional Ising systems

et al. 2002

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“…This allows us to use renormalized 3D quantum field theory to study the Ising model in the scaling region, where lattice effects become negligible and universality holds. This program was initiated by Parisi [1] and has been vigorously pursued to study several aspects of the Ising model [2,3,4]. The agreement between field theoretical calculations and Monte Carlo results is satisfactory.…”

Section: The Case Of the 3d Ising Modelmentioning

confidence: 99%

Interaction effects in the spectrum of the three-dimensional Ising model

Provero

1998

Phys. Rev. E

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The two-point correlation functions of statistical models show in general both poles and cuts in momentum space. The former correspond to the spectrum of massive excitations of the model, while the latter originate from interaction effects, namely creation and annihilation of virtual pairs of excitations. We discuss the effect of such interactions on the long distance behavior of correlation functions in configuration space, focusing on certain time-slice operators which are commonly used to extract the spectrum. For the 3D Ising model in the scaling region of the broken-symmetry phase, a one-loop calculation shows that the interaction effects on time-slice correlations is non negligible for distances up to a few times the correlation length, and should therefore be taken into account when analysing Monte Carlo data.

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“…While the results of [5,6] make use only of series expansions obtained in the symmetric phase of the theory, in [7,8] a three loop calculation, directly performed in the low temperature phase, was used. In this last case a crucial role is played by the low temperature renormalized coupling constant u evaluated at the critical point.…”

Section: Comparison With Other Existing Estimatesmentioning

confidence: 99%

Universal amplitude ratios in the 3D Ising model

Caselle

Hasenbusch

1998

Nuclear Physics B - Proceedings Supplements

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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 studied the model close to criticality in both phases. Great care was taken to control systematic errors due to finite size effects and correction to scaling terms. We obtain C + /C − = 4.75(3), f +,2nd /f −,2nd = 1.95(2) and u * = 14.3(1). Our results are compatible with those obtained by field theoretic methods applied to the φ 4 theory and high and low temperature series expansions of the Ising model. The mismatch with a previous Montecarlo study by Ruge et al. remains to be understood. *

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Field-theoretic calculation of the universal amplitude ratio of correlation lengths in 3D Ising systems

Cited by 25 publications

References 16 publications

Bound states and glueballs in three-dimensional Ising systems

Bound states and glueballs in three-dimensional Ising systems

Interaction effects in the spectrum of the three-dimensional Ising model

Universal amplitude ratios in the 3D Ising model

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