Herbut and Tešanović Reply:

Herbut, Igor F.; Tešanović, Zlatko

doi:10.1103/physrevlett.78.980

Cited by 141 publications

(286 citation statements)

References 4 publications

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“…Dimensional regularization explicitly preserves gauge invariance of the theory implying µ −ǫ Z A e 2 0 = e 2 , to any order. 22,26 In conjunction with this identity and Eq. (9), one can write the (ultraviolet) beta-function of the charge as…”

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confidence: 99%

“…On the other hand, when N f = 0, we obtain the standard one-loop result for the critical number of the complex components of the OP above which the superconductor transition is of the second order, N crit b ≃ 182.952, and the transition is controlled by the charged Wilson-Fisher fixed point, with g 2 * = 0. 22,26 It is worth observing that without the Yukawa interaction, N crit b reduces to 3.47 if one takes only into account the coupling of fluctuating gauge fields with the massless Dirac fermions. 28 The Yukawa coupling therefore appears to be crucial for the stabilization of the criticality in the theory, and for the suppression of the possible discontinuous transition, which occurs in related theories.…”

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Quantum superconducting criticality in graphene and topological insulators

2013

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We correct our previous conclusion regarding the fate of a charged quantum critical point across the superconducting transition for two dimensional massless Dirac fermion. Within the leading order expansion, we now find that the requisite number of four-component Dirac fermion flavors (N f ) for the continuous phase transition through a charged critical point is N f > 18.2699. For N f ≥ 1/2, the critical number of bosonic flavors for this transition is significantly reduced as compared to the value determined in the absence of the Dirac fermions in the theory.

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confidence: 99%

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Quantum superconducting criticality in graphene and topological insulators

2013

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“…The LLL GL model was studied by a variety of different nonperturbative analytical methods. Among them the density functional [10], 1/N [11], elasticity theory [12] and others [13]. The model was also studied numerically in both 3D [14] and 2D [15,16] However we will not discuss those approaches in this paper.…”

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confidence: 99%

Melting of the vortex lattice in high−Tcsuperconductors

Rosenstein

2002

Phys. Rev. B

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“…This is usually interpreted as a sign of a first-order transition [1], [8]. Today, based on accumulated analytical and numerical evidence, it is generally believed that the transition for κ ≫ 1 is again second order, in the so-called inverted-XY universality class [9][10][11][12][13][14][15][16]. The corresponding topology of the flow of the coupling constants under scaling transformation is depicted in Fig.…”

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“…More generally, for small e 2 and b, and for t ≪ e 2 , b, the renormalized couplings obey the differential equations (Eq. 4) with [1,11]:…”

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Effect of order parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

2001

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We show that order-parameter fluctuations in a good type-I superconductor or a liquid crystal always increase the size of the first-order transition. This behavior is eventually changed when the system crosses over to inverted-XY critical behavior, with the size of the first-order transition vanishing as a power law with a crossover exponent. We find good agreement between our theory and a recent experiment on the nematic-smectic-A first-order transition in 8CB-10CB mixtures of liquid crystals.More than 25 years ago, Halperin, Lubensky and Ma (HLM) [1] and Coleman and Weinberg [2] demonstrated that when a scalar field is coupled to a gauge field, the fluctuations of the gauge field can change the nature of the phase transition in the theory from continuous to first order. The coupling of a scalar field (or an order parameter (OP)) to a massless gauge field arises often in physics: the Meissner transition in superconductors [3], the Higgs mechanism in particle physics [4], and the nematic-smectic-A transition in liquid crystals [5] are among the best-known examples [6], [7]. The analysis of HLM initially centered on the fluctuations of the gauge field and neglected the OP fluctuations, which is justifiable for good type-I superconductors (with Ginzburg-Landau parameter κ ≪ 1), where the size (to be precisely defined shortly) of the first-order transition is larger. This approximation, however, inevitably breaks down for strong type-II materials (κ ≫ 1), where neglecting the OP fluctuations would yield a first-order transition well into the critical region. Close to four dimensions, the effect of the OP fluctuations can be studied using the Wilson-Fisher renormalization group [1], which, however, in this case leads only to "run-away" flows and no stable critical points. This is usually interpreted as a sign of a first-order transition [1], [8]. Today, based on accumulated analytical and numerical evidence, it is generally believed that the transition for κ ≫ 1 is again second order, in the so-called inverted-XY universality class [9][10][11][12][13][14][15][16]. The corresponding topology of the flow of the coupling constants under scaling transformation is depicted in Fig. 1. It may thus seem natural to expect that the OP fluctuations should decrease the size of the first-order transition, finally reducing it to zero at the crossover to inverted-XY critical behavior.The fluctuation effects in question are unfortunately too fine to be observable even in high-T c superconductors on account of the smallness of the fine-structure constant [17,18]. But in liquid crystals, the coupling of the smectic OP to the director fluctuations is stronger, and the fluctuations at the nematic-smectic-A transition become an issue of central importance. A recent experiment on twocomponent liquid-crystal mixtures [19] found a surprising result: the size of the first-order transition is larger than the prediction of the HLM theory. Motivated by this result, in this Letter we consider theoretically the effect of OP fluctuations on the ...

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Herbut and Tešanović Reply:

Cited by 141 publications

References 4 publications

Quantum superconducting criticality in graphene and topological insulators

Quantum superconducting criticality in graphene and topological insulators

Melting of the vortex lattice in high−Tcsuperconductors

Effect of order parameter fluctuations on the Halperin-Lubensky-Ma first-order transition in superconductors and liquid crystals

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