We investigate the phase diagram and the nature of the phase transitions of three-dimensional monopole-free ${CP}^{N-1}$ models, characterized by a global $U\left(N\right)$ symmetry, a $U\left(1\right)$ gauge symmetry, and the absence of monopoles. We present numerical analyses based on Monte Carlo simulations for $N=2$, 4, 10, 15, and 25. We observe a finite-temperature transition in all cases, related to the condensation of a local gauge-invariant order parameter. For $N=2$ we are unable to draw any definite conclusion on the nature of the transition. The results may be interpreted in terms of either a weak first-order transition or a continuous transition with anomalously large scaling corrections. However, the results allow us to exclude that the transition belongs to the $O\left(3\right)$ vector universality class, as it occurs in the standard three-dimensional ${CP}^1$ model without monopole suppression. For $N=4,10,\text{and}15$, the transition is of first order, and significantly weaker than that observed in the presence of monopoles. For $N=25$ the results are consistent with a conventional continuous transition. We compare our results with the existing literature and with the predictions of different field-theory approaches. They are consistent with the scenario in which the model undergoes continuous transitions for large values of $N$, including $N=\infty$, in agreement with analytic large-$N$ calculations for the $N$-component Abelian-Higgs model.

中文翻译：

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三维无单极CP ^ {N-1}模型。

我们研究了三相无极子的相图和相变的性质 ${CP}^{ñ-\mathrm{1个}}$ 模式，以全球 $ü（ñ）$ 对称 $ü（\mathrm{1个}）$规范对称，并且没有单极子。我们提出了基于蒙特卡洛模拟的数值分析$ñ=2$，4、10、15和25。在所有情况下，我们都观察到有限的温度转变，这与局部规范不变阶参数的凝聚有关。对于$ñ=2$我们无法就过渡的性质得出任何明确的结论。可以用弱一阶转换或具有异常大的缩放校正的连续转换来解释结果。但是，结果允许我们排除该过渡属于$Ø（3）$ 向量通用性类，因为它出现在标准三维中 ${CP}^{\mathrm{1个}}$无单极抑制的模型。对于$ñ=4，10，\text{和}15$，过渡是一阶的，并且比在单极存在下观察到的要弱得多。对于$ñ=25$结果与常规连续过渡一致。我们将结果与现有文献以及不同领域理论方法的预测进行比较。它们与模型针对较大值的连续经历过渡的情况一致。$ñ$， 包含 $ñ=\infty$，与大型分析$ñ$ 计算 $ñ$分量的Abelian-Higgs模型。