Quantitative picture of the scaling behaviour of lattice nonlinear σ-models from the 1/Nexpansion

Biscari, Paolo; Campostrini, Massimo; Rossi, Paolo

doi:10.1016/0370-2693(90)91462-k

Cited by 45 publications

(37 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(5.24) is [116][117][118] 27) consistently with the exact result (4.15). In the same limit one may also show that 28) and the on-shell renormalization condition can be imposed on Z.…”

Section: Mass and Wavefunction Renormalizationsupporting

confidence: 78%

“…[116,149]. Higher-order coefficients of the weak coupling series can be evaluated numerically with high precision, and different truncations of the series can be compared, checking for stability.…”

Section: Evaluation Of Physical Quantities For Nearest-neighbor Intermentioning

confidence: 99%

“…However some computations can only be, to the best of our knowledge, performed numerically [116,148]:…”

mentioning

confidence: 99%

See 2 more Smart Citations

The 1/N expansion of two-dimensional spin models

Campostrini

Rossi

1993

Riv. Nuovo Cim.

View full text Add to dashboard Cite

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.

show abstract

“…(5.24) is [116][117][118] 27) consistently with the exact result (4.15). In the same limit one may also show that 28) and the on-shell renormalization condition can be imposed on Z.…”

Section: Mass and Wavefunction Renormalizationsupporting

confidence: 78%

Section: Evaluation Of Physical Quantities For Nearest-neighbor Intermentioning

confidence: 99%

See 1 more Smart Citation

The 1/N expansion of two-dimensional spin models

Campostrini

Rossi

1993

Riv. Nuovo Cim.

View full text Add to dashboard Cite

show abstract

“…[8]. The discussion of our methods and results and a cokparison with numerical evaluations will be the subject of a separate paper in preparation.…”

Section: Introductionmentioning

confidence: 97%

Monte Carlo simulation ofCPN−1models

1992

Self Cite

View full text Add to dashboard Cite

Numerical simulations of two-dimensional CpN-' models are performed at N = 2, 10, and 21. The lattice action adopted depends explicitly on the gauge degrees of freedom and shows precocious scaling. Our tests of scaling are the stability of dimensionless physical quantities (second moment of the correlation function versus inverse mass gap, magnetic susceptibility versus square correlation length) and rotation invariance. Topological properties of the models are explored by measuring the topological susceptibility and by extracting the Abelian string tension. Several different (local and nonlocal) lattice definitions of topological charge are discussed and compared. The qualitative physical picture derived from the continuum 1/N expansion is confirmed, and agreement with quantitative 1/N predictions is satisfactory. Variant (Symanzik-improved) actions are considered in the CP1 = O(3) case and agreement with universality and previous simulations (when comparable) is found. The simulation algorithm is an efficient mixture of over-heat-bath and microcanonical algorithms. The dynamical features and critical exponents of the algorithm are discussed in detail.

show abstract

“…It can be solved in the N = ∞ limit [18,19] and 1/N corrections can be systematically calculated [20][21][22]. An exact S-matrix can be computed [23,24] and, using the thermodynamic Bethe ansatz, the exact mass gap of the theory in the limit β → ∞ has been obtained [25,26].…”

Section: Introductionmentioning

confidence: 99%

Testing the efficiency of different improvement programs

Caracciolo¹,

Montanari²,

Pelissetto³

1999

Nuclear Physics B

View full text Add to dashboard Cite

We study the finite-size behaviour of a tree-level on-shell improved action for the N -vector model. We present numerical results for N = 3 and analytic results in the large-N limit for the mass gap. We also report a perturbative computation at one loop of the mass gap for states of spatial momentum p. We present a detailed comparison of the behaviour of this action with that of other formulations, including the perfect action, and a critical discussion of the different approaches to the problem of action improvement.

show abstract

Quantitative picture of the scaling behaviour of lattice nonlinear σ-models from the 1/Nexpansion

Cited by 45 publications

References 32 publications

The 1/N expansion of two-dimensional spin models

The 1/N expansion of two-dimensional spin models

Monte Carlo simulation ofCPN−1models

Testing the efficiency of different improvement programs

Contact Info

Product

Resources

About