Comparison of the O(3) bootstrap σ model with lattice regularization at low energies

Balog, J.; Niedermaier, M.; Niedermayer, Ferenc; Patrascioiu, Adrian; Seiler, Erhard; Weisz, Peter

doi:10.1103/physrevd.60.094508

Cited by 37 publications

(61 citation statements)

References 39 publications

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“…In the limit of small x we have 8) consistent with the general result (3.15) for l = 1, 2, the scalar Adler function in the leading order 1/n being just A 0 (z) = (1+M 2 /z) −2 . Note the limit is approached extremely slowly.…”

Section: The Spin Field Structure Functionssupporting

confidence: 72%

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Structure functions of the 2d non-linear sigma models

Balog

Weisz

2005

Nuclear Physics B

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We investigate structure functions in the 2-dimensional (asymptotically free) nonlinear O(n) σ-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n = 3 model are accurately computed over the whole x range for −q 2 /M 2 < 10 5 , and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.

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Section: The Spin Field Structure Functionssupporting

confidence: 72%

“…The possible equivalence of this construction to the continuum limit of the lattice regularized theory has been investigated in ref. [8].…”

Section: O(n) Model and Structure Functionsmentioning

confidence: 99%

Structure functions of the 2d non-linear sigma models

Balog

Weisz

2005

Nuclear Physics B

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“…[6] an alternative was suggested which starts from the observation that the relative momentum 2p n of the two particles is also encoded in the wave function: in the symmetric channels (I = 0, 2) one should have 9) and similarly with sin p n (x − L/2) for the I = 1 channel. Here R is the "interaction range" characterized by the requirement that for a relative distance x > R the two particles propagate essentially freely.…”

Section: Phase Shiftsmentioning

confidence: 99%

“…To avoid the instability, we restrict first the correlation matrix to an M-dimensional subspace (M < N) spanned by the first M eigenvectors of C(t 0 ) with the largest eigenvalues (still stable against the statistical fluctuations) [6,37]. The generalized eigenvalue problem is then written for the new correlation matrix C(t) in this reduced basis.…”

Section: Phase Shiftsmentioning

confidence: 99%

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Does the XY model have an integrable continuum limit?

et al. 2001

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The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.

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Topological lattice actions

Bietenholz¹,

Gerber²,

Wiese³

2010

J. High Energ. Phys.

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We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility χ t = Q 2 /V is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.

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Comparison of the O(3) bootstrap σ model with lattice regularization at low energies

Cited by 37 publications

References 39 publications

Structure functions of the 2d non-linear sigma models

Structure functions of the 2d non-linear sigma models

Does the XY model have an integrable continuum limit?

Topological lattice actions

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