Monte Carlo simulation ofCPN−1models

Abstract

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.

θ dependence of SU(N) gauge theories in the presence of a topological term

“…[281,282,363,364,456] for the 4D SU (2) and SU (3) lattice gauge theories, and in Refs. [75,124,125,193,338,533,554] for the 2D CP N −1 models.…”

Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

“…Over the past decade there has been much interest in two-dimensional lattice σ-models taking values in the real projective space RP N −1 [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], the complex projective space CP N −1 [1,17,4,18,19,20,21,22,23,24] or the quaternionic projective space QP N −1 [25]. 1 These models are good laboratories for investigating asymptotic freedom, topological phenomena and universality; they are intermediate in complexity between two-dimensional N-vector models (σ-models taking values in the sphere S N −1 ) and four-dimensional non-abelian gauge theories.…”

Scaling and topology in the 2-d 0(3) σ-model on the lattice with the fixed point action

“…[30]). [12]), field theoretical method and CP 1 standard action with explicit gauge degrees of freedom (column (3), [34]), FP charge operator and parametrized FP action 10 (column (4), [13]). …”

“…Data in columns (2) and (3) have been obtained in the field theoretical approach with the standard definition of the topological charge operator, but using other lattice regularizations of the action [12] [34]. In column (4) a parametrized FP action and the FP lattice charge operator have been used.…”