Phase structure and phase transitions in a three-dimensionalSU(2)superconductor

Abstract

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.

Lattice Abelian-Higgs model with noncompact gauge fields

“…Indeed, the numerical results reported in Refs. [22,23,30] confirm that the transitions along the CH line are of first order, at least for κ not too large (they apparently disagree only far from the multicritical point). To clarify whether the bicritical transition is continuous or of first order, it is necessary to analyze the RG flow of the multicritical 4 theory ( 23): The multicritical transition can be continuous only if a stable fixed point can be associated with the bicritical point.…”

“…In particular, for N = 2, theoretical and numerical investigations of classical and quantum transitions, which are expected to be in the same universality class as those occurring in non-compact scalar electrodynamics, have provided evidence of weakly first-order or continuous transitions belonging to a new universality class (see, e.g., Refs. [7,[9][10][11][12][13][14][15][16][17][18][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]).…”

Corrections to scaling in the critical theory of deconfined criticality

“…(2) and related spin models such as the sign-problem free J −Q model seem to favor the possibility of a continuous phase transition at a nonzero charge, as hypothesized by the theory of deconfined criticality, [21][22][23][24][25][26][27][28][29] other studies are undecided 30 or report weakly first-order phase transitions. [31][32][33][34] Unexpected corrections to scaling were reported by Sandvik, 26 and it is our aim here to understand the critical theory and its corrections to scaling from an RG perspective.…”

Higher-charge three-dimensional compact lattice Abelian-Higgs models

“…For example, the critical behavior of the lattice CP N−1 model, which is the simplest classical model with U(1) gauge symmetry, depends on the presence/absence of topological defects [23][24][25][26][27], such as monopoles, both for N = 2 and large values of N. Analogous differences emerge in the behavior of compact and noncompact lattice formulations of scalar electrodynamics, i.e., of the multicomponent Abelian-Higgs model; see, e.g., Refs. [12,[14][15][16][17][18][19][20][21][22][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”