Currents in superfluid 3He

Golo, V. L.; Monastyrsky, Michael

doi:10.1007/bf00400163

Cited by 13 publications

(13 citation statements)

References 3 publications

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“…After much thought, we decided to study a two-parameter model of two-dimensional spin fields with U(N) global symmetry [7]. This model interpolates between the standard O(2N) [8][9][10] and CP N −1 models [11,12], and for special values of the parameters it represents the gauge-fixed bosonized version of the minimal coupling of massless fermions to CP N −1 fields [13].…”

Section: Introductionmentioning

confidence: 99%

The 1/N expansion of two-dimensional spin models

Campostrini

Rossi

1994

Nuclear Physics B - Proceedings Supplements

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A short review of all available results (perturbative, nonperturbative, and exact) on d-dimensional spin models is presented in order to introduce the discussion of their 1/N expansion at d = 2, where the models are asymptotically free.A general two-dimensional spin model with U(N ) invariance, interpolating between CP N −1 and O(2N ) models, is studied in detail in order to illustrate both the general features of the 1/N expansion on the lattice and the specific techniques devised to extract scaling (field-theoretical) behavior.The continuum version of the model is carefully analyzed deriving quantitative O(1/N ) physical predictions in order to establish a benchmark for lattice computations.The 1/N expansion on the lattice, including second-nearest-neighbor interactions, is set up by constructing explicitly effective propagators and vertices, and exhibiting a number of exact results and integral representations that allow a substantial reduction of the numerical effort. The technique of asymptotic expansion of the lattice propagators, basic to the derivation of analytical results in the scaling domain, is presented in full detail and applied to the model. Physical quantities, like the free energy and different definitions of correlation length, are evaluated.The lattice renormalization-group trajectories are identified and universality among different lattice (and continuum) schemes in the scaling region is explicitly proven. As a byproduct, representations of the O(1/N ) contribution to the Λ-parameter ratios and to the lattice β functions are obtained.A review of other developments based on the lattice 1/N expansion (finite size scaling, higher orders, fermionic models) is presented.

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Section: Introductionmentioning

confidence: 99%

The 1/N expansion of two-dimensional spin models

Campostrini

Rossi

1994

Nuclear Physics B - Proceedings Supplements

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“…Skyrmions are good toy models [121] for some aspects of the Yang-Mills theory of the strong and electroweak forces (instantons, θ-vacua and topological quantum numbers). On the other hand: nonlinear sigma models [122,123] usefully model a number of aspects of diffeomorphisms and of string-theoretic target spaces. CP 2 is here present in its quotient form as the target space.…”

Section: Motivating Rpm Models In Generalmentioning

confidence: 99%

Relational Quadrilateralland I: The Classical Theory

Anderson

Kneller

2014

Int. J. Mod. Phys. D

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Relational particle mechanics (RPM) models bolster the relational side of the absolute versus relational motion debate. They are additionally toy models for the dynamical formulation of General Relativity (GR) and its Problem of Time (PoT). They cover two aspects that the more commonly studied minisuperspace GR models do not: 1) by having a nontrivial notion of structure and thus of cosmological structure formation and of localized records. 2) They have linear as well as quadratic constraints, which is crucial as regards modelling many PoT facets.I previously solved relational triangleland classically, quantum mechanically and as regards a local resolution of the PoT. This rested on triangleland's shape space being S 2 with isometry group SO(3), allowing for use of widely-known Geometry, Methods and Atomic/Molecular Physics analogies. I now extend this work to the relational quadrilateral, which is far more typical of the general N -a-gon, represents a 'diagonal to nondiagonal Bianchi IX minisuperspace' step-up in complexity, and encodes further PoT subtleties. The shape space now being CP 2 with isometry group SU (3)/Z3, I now need to draw on Geometry, Shape Statistics and Particle Physics to solve this model; this is therefore an interdisciplinary paper. This Paper treats quadrilateralland at the classical level, and then Paper II provides a quantum treatment.

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“…The WZW model gives a model of conformal field theory whose current algebra is realized by a Kac-Moody algebra. The massive chiral model, which is the chiral Lagrangian [6,7] or the non-linear sigma model with the mass term, is also interesting as a two-dimensional field theory. The massive chiral model can be regarded as a generalization of the sine-Gordon model to the model for G-valued fields [8], where we add the term of type Tr(g + g −1 ) for g ∈ G where G is a general gauge group (Lie group).…”

Section: Introductionmentioning

confidence: 99%

Chiral sine-Gordon model

Yanagisawa¹

2016

EPL

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We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for G-valued fields and describes a new class of phase transitions, where G is a compact Lie group. We show that the model is renormalizable by means of a perturbation expansion and we derive beta functions of the renormalization group theory. The coefficients of beta functions are represented by the Casimir invariants. The model contains both asymptotically free and ultraviolet strong coupling regions. The beta functions have a zero which is a bifurcation point that divides the parameter space into two regions; they are the weak coupling region and the strong coupling region. A large-N model is also considered. This model is reduced to the conventional sine-Gordon model that describes the Kosterlitz-Thouless transition near the fixed point. In the strong-coupling limit, the model is reduced to a U (N ) matrix model.

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Currents in superfluid 3He

Cited by 13 publications

References 3 publications

The 1/N expansion of two-dimensional spin models

The 1/N expansion of two-dimensional spin models

Relational Quadrilateralland I: The Classical Theory

Chiral sine-Gordon model

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