We consider a three dimensional lattice U͑1͒ ϫ U͑1͒ and ͓U͑1͔͒ N superconductors in the London limit with individually conserved condensates. The U͑1͒ ϫ U͑1͒ problem, generically, has two types of intercomponent interactions of different characters. First, the condensates are interacting via a minimal coupling to the same fluctuating gauge field. A second type of coupling is the direct dissipationless drag represented by a local intercomponent current-current coupling term in the free-energy functional. In this work, we present a study of the phase diagram of a U͑1͒ ϫ U͑1͒ superconductor which includes both of these interactions. We study phase transitions and two types of competing paired phases which occur in this general model: ͑i͒ a metallic superfluid phase ͑where there is order only in the gauge-invariant phase difference of the order parameters͒, ͑ii͒ a composite superconducting phase where there is order in the phase sum of the order parameters which has many properties of a single-component superconductor but with a doubled value of electric charge. We investigate the phase diagram with particular focus on what we call "preemptive phase transitions." These are phase transitions unique to multicomponent condensates with competing topological objects. A sudden proliferation of one kind of topological defects may come about due to a fluctuating background of topological defects in other sectors of the theory. For U͑1͒ ϫ U͑1͒ theory with unequal bare stiffnesses where components are coupled by a noncompact gauge field only, we study how this scenario leads to a merger of two U͑1͒ transitions into a single U͑1͒ ϫ U͑1͒ discontinuous phase transition. We also report a general form of vortexvortex bare interaction potential and possible phase transitions in an N-component London superconductor with individually conserved condensates.

Utilizing large-scale Monte-Carlo simulations, we investigate an unconventional two-component classical plasma in two dimensions which controls the behavior of the norms and overlaps of the quantum-mechanical wavefunctions of Ising-type quantum Hall states. The plasma differs fundamentally from that which is associated with the two-dimensional XY model and Abelian fractional quantum Hall states. We find that this unconventional plasma undergoes a Berezinskii-KosterlitzThouless phase transition from an insulator to a metal. The parameter values corresponding to Ising-type quantum Hall states lie on the metallic side of this transition. This result verifies the required properties of the unconventional plasma used to demonstrate that Ising-type quantum Hall states possess quasiparticles with non-Abelian braiding statistics.

We study the three dimensional SU(2)-symmetric noncompact CP 1 model, with two charged matter fields coupled minimally to a noncompact Abelian gauge-field. The phase diagram and the nature of the phase transitions in this model have attracted much interest after it was proposed to describe an unusual continuous transition associated with deconfinement of spinons. Previously, it has been demonstrated for various two-component gauge theories that weakly first-order transitions may appear as continuous ones of a new universality class in simulations of relatively large, but finite systems. We have performed Monte-Carlo calculations on substantially larger systems sizes than those in previous works. We find that in some area of the phase diagram where at finite sizes one gets signatures consistent with a single first-order transition, in fact there is a sequence of two phase transitions with an O(3) paired phase sandwiched in between. We report (i) a new estimate for the location of a bicritical point and (ii) the first resolution of bimodal distributions in energy histograms at relatively low coupling strengths. We perform a flowgram analysis of the direct transition line with rescaling of the linear system size in order to obtain a data collapse. The data collapses up to coupling constants where we find bimodal distributions in energy histograms.

We study an unconventional two-dimensional, two-component classical plasma on a sphere, with emphasis on detecting signatures of melting transitions. This system is relevant to Ising-type quantum Hall states, and is unconventional in the sense that it features particles interacting via two different two-dimensional Coulomb interactions. One species of particles in the plasma carries charge of both types (Q1, Q2), while the other species carries only charge of the second type (0, −Q2). We find signatures of a freezing transition at Q 2 1140. This means that the species with charge of both types will form a Wigner crystal, whereas the species with charge of the second type also shows signatures of being a Wigner crystal, due to the attractive inter-component interaction of the second type. Moreover, there is also a Berezinskii-Kosterlitz-Thouless phase transition at Q 2 2 4, at which the two species of particles bind to form molecules that are neutral with respect to the second Coulomb interaction. These two transitions appear to be independent of each other, giving a rectangular phase diagram. As a special case, Q2 = 0 describes the (conventional) two-dimensional one-component plasma. Our study is consistent with previous studies of this plasma, and sheds new light on the freezing transition of this system.

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