Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

Ono, T.; Doi, Shunsuke; Hori, Yuki; Ichinose, Ikuo; Matsui, Tetsuo

doi:10.1016/j.aop.2009.09.002

Cited by 12 publications

(4 citation statements)

References 30 publications

(37 reference statements)

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“…We also mention that some numerical results for the AH lattice model (3) have been reported in Refs. [6,21,22], but a definite picture has not been achieved yet [23].…”

Section: Introductionmentioning

confidence: 99%

Multicomponent compact Abelian-Higgs lattice models

Pelissetto

Vicari

2019

Phys. Rev. E

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We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N -component complex field z a x of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation. We determine the phase diagram and study the nature of the transition line for N = 2 and N = 4. Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q ab x = z a x z bx − δ ab /N , which plays the role of order parameter. In one phase, we have Q ab x = 0, while in the other Q ab x condenses. Gauge correlations are never critical: gauge excitations are massive for any finite coupling. The two phases are separated by a transition line. Our numerical data are consistent with the simple scenario in which the nature of the transition is independent of the gauge coupling. Therefore, for any finite positive value of the gauge coupling, we predict a continuous transition in the Heisenberg universality class for N = 2 and a first-order transition for N = 4. However, notable crossover phenomena emerge for large gauge couplings, when gauge fluctuations are suppressed. Such crossover phenomena are related to the unstable O(2N ) fixed point, describing the behavior of the model in the infinite gauge-coupling limit.

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“…We also mention that some numerical results for the AH lattice model (3) have been reported in Refs. [6,21,22], but a definite picture has not been achieved yet [23].…”

Section: Introductionmentioning

confidence: 99%

Multicomponent compact Abelian-Higgs lattice models

Pelissetto

Vicari

2019

Phys. Rev. E

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“…Its phase diagram has been thoroughly investigated in three dimensions, considering both the compact and noncompact formulation of electrodynamics, see, e.g., Refs. [2,[5][6][7][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. On the other hand, multicomponent lattice AH systems have been much less considered in two dimensions.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional multicomponent Abelian-Higgs lattice models

2020

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We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an N -component complex scalar field, characterized by a global SU(N ) symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature and a critical behavior is only observed in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice N -component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D CP N−1 field theory.

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“…Here let us comment on the 3D multi-component Higgs model in the compact version with N Higgs fields in the London limit 18 . In contrast to the above 3D model with N = 1, the model with N ≥ 2 supports the Higgs phase due to the extra phase degrees of freedom that are free from coupling to the gauge field.…”

Section: Lattice Model For Fmsc State a Lattice Gauge-higgs Model For...mentioning

confidence: 99%

“…In the 4D compact case, there is a gauge transition from the confinement phase to the Coulomb phase as 1/e 2 increases and a Higgs transition from the Coulomp phase to the Higgs phase as K ′ increases 17 . Here let us comment on the 3D multi-component Higgs model in the compact version with N Higgs fields in the London limit 18 . In contrast to the above 3D model with N = 1, the model with N ≥ 2 supports the Higgs phase due to the extra phase degrees of freedom that are free from coupling to the gauge field.…”

Section: Lattice Model For Fmsc State a Lattice Gauge-higgs Modementioning

confidence: 99%

Lattice Ginzburg-Landau model of a ferromagneticp-wave pairing phase in superconducting materials and an inhomogeneous coexisting state

et al. 2012

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We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge-Higgs model for the s-wave SC transition, and study it numerically by Monte-Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region where the two transition temperatrures satisfy TFM > TSC. For TFM/TSC < 0.7, we find that the coexisting region of FM and SC orders appears only near the surface of the lattice, which describes an inhomogeneous FMSC coexisting state.

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Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

Abstract: We study the three-dimensional (3D) compact U (1)

Cited by 12 publications

References 30 publications

Multicomponent compact Abelian-Higgs lattice models

Multicomponent compact Abelian-Higgs lattice models

Two-dimensional multicomponent Abelian-Higgs lattice models

Lattice Ginzburg-Landau model of a ferromagneticp-wave pairing phase in superconducting materials and an inhomogeneous coexisting state

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