Monte Carlo simulation of lattice ${\mathrm{CP}}^{N-1}$ models at large N

Abstract

In order to check the validity and the range of applicability of the 1/N expansion, we performed numerical simulations of the two-dimensional lattice CP(N-1) models at large N, in particular we considered the CP(20) and the CP(40) models. Quantitative agreement with the large-N predictions is found for the correlation length defined by the second moment of the correlation function, the topological susceptibility and the string tension. On the other hand, quantities involving the mass gap are still far from the large-$N$ results showing a very slow approach to the asymptotic regime. To overcome the problems coming from the severe form of critical slowing down observed at large N in the measurement of the topological susceptibility by using standard local algorithms, we performed our simulations implementing the Simulated Tempering method.

4 pages

Cited by in corpus (20)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Critical slowing down of topological modes
• Spectrum of confining strings in SU(N) gauge theories
• k-string tensions in SU(N) gauge theories
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Topological critical slowing down: variations on a toy model
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Monte Carlo Studies of Two-Dimensional Systems with a $\theta$ Term
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Finite size scaling in CP(N-1) models
• Irreversible simulated tempering
• Theta-vacuum and large N limit in CP^{N-1} sigma models
• The topological properties of QCD at high temperature: problems and perspectives
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model