Bound states and glueballs in three-dimensional Ising systems

Caselle, Michele; Hasenbusch, Martin; Provero, Paolo; Zarembo, Konstantin

doi:10.1016/s0550-3213(01)00644-7

Cited by 48 publications

(79 citation statements)

References 16 publications

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“…In the weakly coupled regime, the existence of these states follows from the fact that the λϕ 4 interaction becomes attractive in the broken phase, the cubic exchange diagrams overwhelming the repulsive effect of the contact term interaction [36]. Their binding energy, exponentially small at weak coupling, is known in the leading and first subleading exponential approximation [36,37]. Apparently, here we are observing the same effect in d ¼ 2.5 dimensions and at strong coupling.…”

supporting

confidence: 63%

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

2015

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We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the truncated conformal space approach, a Hamiltonian method which exploits the conformal structure of the UV fixed point. The theory is regulated in the IR by putting it on a sphere of a large finite radius. The quantum field theory Hamiltonian is expressed as a matrix in the Hilbert space of conformal field theory states. After restricting ourselves to energies below a certain UV cutoff, an approximation to the spectrum is obtained by numerical diagonalization of the resulting finite-dimensional matrix. The cutoff dependence of the results can be computed and efficiently reduced via a renormalization procedure. We work out the details of the method for the ϕ 4 theory in d dimensions with d being not necessarily integer. A numerical analysis is then performed for the specific case d ¼ 2.5, a value chosen in the range where UV divergences are absent. By going from weak to intermediate to strong coupling, we are able to observe the symmetry-preserving, symmetry-breaking, and conformal phases of the theory, and perform rough measurements of masses and critical exponents. As a byproduct of our investigations we find that both the free and the interacting theories in nonintegral d are not unitary, which however does not seem to cause much effect at low energies.

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supporting

confidence: 63%

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

2015

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“…If universality would apply in strict sense, these spectra should exhibit the same pattern, as suggested by several numerical determinations in the 3d Ising class [20,21,22,23].…”

Section: Introductionsupporting

confidence: 57%

Screening masses in the SU(3) pure gauge theory and universality

et al. 2007

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We determine from Polyakov loop correlators the screening masses in the deconfined phase of the (3+1)d SU(3) pure gauge theory at finite temperature near the transition, for two different channels of angular momentum and parity. Their ratio is compared with that of the massive excitations with the same quantum numbers in the 3d 3-state Potts model in the broken phase near the transition point at zero magnetic field. Moreover we study the inverse decay length of the correlation between the real parts and between the imaginary parts of the Polyakov loop and compare the results with expectations from perturbation theory and mean-field Polyakov loop models.

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“…and analogous relations hold for other observables; in particular, it is interesting to see that the Z 2 gauge theory glueballs can be interpreted in terms of bound states of the fundamental scalar in the spin model [35]. In the case of our interest, adding external source terms for the gauge model (for instance, a pair of Polyakov loops) amounts to introducing sets of topological defects in the spin system.…”

Section: General Setting and The Algorithmmentioning

confidence: 88%

On the effective string spectrum of the tridimensional Bbb Z₂gauge model

Caselle

Hasenbusch

Panero

2006

J. High Energy Phys.

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We study the Z 2 lattice gauge theory in three dimensions, and present high precision estimates for the first few energy levels of the string spectrum. These results are obtained from new numerical data for the two-point Polyakov loop correlation function, which is measured in the 3d Ising spin system using duality. This allows us to perform a stringent comparison with the predictions of effective string models. We find a remarkable agreement between the numerical estimates and the Nambu-Goto predictions for the energy gaps at intermediate and large distances. The precision of our data allows to distinguish clearly between the predictions of the full Nambu-Goto action and the simple free string model up to an interquark distance r ≈ 10/ √ σ. At the same time, our results also confirm the breakdown of the effective picture at short distances, supporting the hypothesis that terms which are not taken into account in the usual Nambu-Goto string formulation yield a non-trivial shift to the energy levels. Furthermore, we discuss the theoretical implications of these results.

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Bound states and glueballs in three-dimensional Ising systems

Cited by 48 publications

References 16 publications

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

Screening masses in the SU(3) pure gauge theory and universality

On the effective string spectrum of the tridimensional Bbb Z₂gauge model

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Bound states and glueballs in three-dimensional Ising systems

Cited by 48 publications

References 16 publications

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

Screening masses in the SU(3) pure gauge theory and universality

On the effective string spectrum of the tridimensional Bbb Z2gauge model

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Product

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On the effective string spectrum of the tridimensional Bbb Z₂gauge model