Simulation of a Scalar Field on a Fuzzy Sphere

Flores, Fernando García; Martín, Xavier; O’Connor, Denjoe

doi:10.1142/s0217751x09043195

Cited by 47 publications

(92 citation statements)

References 38 publications

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“…Comparing with previous studies of scalar field theories on fuzzy spaces [2,3] as well as the numerical results of [11,[17][18][19], we expect three phases: a symmetric single cut solution, in which the eigenvalue density has support on a single symmetric interval…”

Section: Phase Diagramsupporting

confidence: 62%

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The phase diagram of scalar field theory on the fuzzy disc

Rea¹,

Sämann²

2015

J. High Energ. Phys.

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Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.

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Section: Phase Diagramsupporting

confidence: 62%

“…the numerical results of [21]. Scalar field theories on two-dimensional fuzzy spaces necessarily inherit this phase transition, and the straight line was found in the numerical studies of [11,[17][18][19] on the fuzzy sphere and the fuzzy disc. We reproduced this line by analytical methods.…”

Section: Comparison To Numerical Resultsmentioning

confidence: 91%

The phase diagram of scalar field theory on the fuzzy disc

Rea¹,

Sämann²

2015

J. High Energ. Phys.

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“…Several works [13,14,15,16,25,49] studied the phase structure of NC φ 4 theory in two dimensions, finding numerical evidence for a striped phase [50] characterized by non-uniform order. As an example, fig.…”

Section: Results For Nc Scalar Field Theorymentioning

confidence: 99%

“…This type of calculation has been carried out by Monte Carlo methods in a number of works [13,14,15,16,17] (including a very recent study of the entanglement entropy [18]). A different way to map NC scalar field theory in two dimensions to a finite-dimensional matrix model was introduced in ref.…”

Section: Methodsmentioning

confidence: 99%

The numerical approach to quantum field theory in a noncommutative space

Panero¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is presented, and their implications are reviewed. In addition, we also discuss how related numerical techniques have been recently applied in computer simulations of dimensionally reduced supersymmetric theories.

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“…The phase structure of non-commutative φ 4 in d = 2 and d = 3 using as a regulator the fuzzy sphere was studied extensively in [76][77][78][79][80][81][82]. It was confirmed that the phase diagram consists of three phases: a disordered phase, a uniform ordered phases and a non-uniform ordered phase which meet at a triple point.…”

Section: Introductionmentioning

confidence: 99%

Wilson RG of noncommutative Φ44

Ydri

Ahmim

Bouchareb

2015

Int. J. Mod. Phys. A

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We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large N . Three fixed points are identified. The matrix model θ = ∞ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at θ = 0 which describes the disordered-to-uniformordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of θ which is associated with the transition between non-uniform-order and uniform-order phases. IntroductionA noncommutative field theory is a non-local field theory in which we replace the ordinary local point-wise multiplication of fields with the non-local Moyal-Weyl star product [1,2]. This product is intimately related to coherent states [6][7][8], Berezin quantization [9] and deformation quantization [10]. It is also very well understood that the underlying operator/matrix structure of the theory, exhibited by the Weyl map [5], is the singular most important difference with commutative field theory since it is at the root cause of profound physical differences between the two theories. We suggest [3] and references therein for elementary and illuminating discussion of the Moyal-Weyl product and other star products and their relations to the Weyl map and coherent states.Noncommutative field theory is believed to be of importance to physics beyond the standard model and the Hall effect [34] and also to quantum gravity and string theory [35,36]. * Email:ydri@stp.dias.ie, badis.ydri@univ-annaba.org. 1Noncommutative scalar field theories are the most simple, at least conceptually, quantum field theories on noncommutative spaces. Some of the novel quantum properties of noncommutative scalar field theory and scalar phi-four theory are as follows:

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Simulation of a Scalar Field on a Fuzzy Sphere

Cited by 47 publications

References 38 publications

The phase diagram of scalar field theory on the fuzzy disc

The phase diagram of scalar field theory on the fuzzy disc

The numerical approach to quantum field theory in a noncommutative space

Wilson RG of noncommutative Φ44

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