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The phase diagram and critical properties of the $N$-component Londonsuperconductor are studied both analytically and through large-scaleMonte-Carlo simulations in $d=2+1$ dimensions (components here refer todifferent replicas of the complex scalar field). Examples are given of physicalsystems to which this model is applicable. The model with different bare phasestiffnesses for each component, is a model of superconductivity which shouldarise out of metallic phases of light atoms under extreme pressure. A projectedmixture of electronic and protonic condensates in liquid metallic hydrogenunder extreme pressure is the simplest example, corresponding to N=2. These aresuch that Josephson coupling between different matter field components {\it isprecisely zero on symmetry grounds}. The $N$-component London model is dualizedto a theory involving $N$ vortex fields with highly nontrivial interactions. Wecompute critical exponents $\alpha$ and $\nu$ for N=2 and N=3. Direct and dualgauge field correlators for general $N$ are given and the N=2 case is studiedin detail. The model with N=2 shows two anomalies in the specific heat when thebare phase stiffnesses of each matter field species are different. One anomalycorresponds to an {\it inverted} \xy fixed point, while the other correspondsto a \xy fixed point. Correspondingly, for N=3, we demonstrate the existence oftwo neutral \xy fixed points and one inverted charged \xy fixed point.Comment: 46 pages, 34 figures, 3 tables. Two new figures (figures 21 and 22).  References added and updated. To be published in Physical Review

physical review. b, condensed matter and materials physics

Field- and temperature-induced topological phase transitions in the three-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-component London superconductor

Field- and temperature-induced topological phase transitions in the three-dimensionalN-component London superconductor