Large-N behavior of three-dimensional lattice CP(N-1) models

Abstract

We investigate the phase diagram and critical behavior of a three-dimensional lattice CP(N-1) model in the large-N limit. Numerical evidence of first-order transitions is always observed for sufficiently large values of N, i.e. N>2 up to N=100. The transition becomes stronger---both the latent heat and the surface tension increase---as N increases. Moreover, on the high-temperature side, gauge fields decorrelate on distances of the order of one lattice spacing for all values of N considered. Our results are consistent with a simple scenario, in which the transition is of first order for any N, including N=\infty. We critically discuss the analytic large-N calculations that predicted a large-N continuous transition, showing that one crucial assumption made in these computations fails for the model we consider.

arXiv comment15 pages

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• Lattice gauge theories in the presence of a linear gauge-symmetry breaking
• Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories
• Three-dimensional monopole-free CP(N-1) models
• Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
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• Deconfined criticality and bosonization duality in easy-plane Chern-Simons two-dimensional antiferromagnets
• Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields
• Three-dimensional monopole-free CP${}^{N-1}$ models: Behavior in the presence of a quartic potential
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• Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry
• One-loop effective action of the $\mathbb{C}{P}^{N-1}$ model at large $\mu \beta$
• Modified Abelian and SU(2) Wilson theories on a lattice from a non-compact regularization