Electromagnetic fluxes, monopoles, and the order of 4d compact U(1) phase transition

Vettorazzo, Michele; Forcrand, Philippe de

doi:10.1016/j.nuclphysb.2004.02.038

Cited by 43 publications

(58 citation statements)

References 35 publications

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“…We compare these results with the corresponding observables obtained with the Wilson action in figures 5 and 6: it is obvious that the transition is even weaker than the weak first order transition seen with the Wilson action. We can try to quantify the strength of the transition by fitting the helicity modulus in the confining phase using a simple model of a first order transition [15,17] …”

Section: Resultsmentioning

confidence: 99%

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U(1) lattice gauge theory with a topological action

Akerlund

Forcrand

2015

J. High Energ. Phys.

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Abstract:We investigate the phase diagram of the compact U(1) lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. However, since the monopoles do not influence the long-distance properties of the Coulomb phase, the physics is smooth across the singularity in the monopole density. The topological action offers an algorithmic advantage for the computation of the free energy.

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Section: Resultsmentioning

confidence: 99%

“…This can be measured by promoting the flux to a dynamical variable, which is updated along with the link angles [12]. By measuring the probability distribution p(φ) (via a histogram method for example) of the visited fluxes one thus obtains the full 2π periodic free energy [15] and the helicity modulus…”

Section: Jhep06(2015)183mentioning

confidence: 99%

U(1) lattice gauge theory with a topological action

Akerlund

Forcrand

2015

J. High Energ. Phys.

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“…Differences in action values obtained after ordered and disordered starts support a non-zero latent heat in the infinite volume limit. For N τ = 6 the spatial lattice sizes used are N s = 48 and 60 and their MC statistics shown consists of 5 000 measurements per run, separated by one heatbath plus four overrelaxation sweeps (these units are not defined in [18], but were communicated to us by de Forcrand and previously used in [15]). For a second order phase transition the integrated autocorrelation time τ int scales approximately ∼ N 2 s and we estimate from our own simulations on smaller lattices that in units of those measurements τ int ≈ 7 000 for N τ = 6 and N s = 48.…”

Section: Numerical Resultsmentioning

confidence: 99%

Nonperturbative U(1) gauge theory at finite temperature

Berg

Bazavov

2006

Phys. Rev. D

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For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on Nτ N 3 s lattices for Nτ fixed by extrapolating spatial volumes of size Ns ≤ 18 to Ns → ∞. Within the numerical accuracy of the thus obtained fits we find for Nτ = 4, 5 and 6 second order critical exponents, which exhibit no obvious Nτ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.

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“…There is a transition but is it first or second order? Despite some earlier suggestions of a second order transition [21,22], there seems to be a general agreement that the transition is first order [26,27,28]. This question has been revisited recently from the point of view of Fisher zeros [29].…”

Section: Model Calculationsmentioning

confidence: 97%

Fisher zeros and conformality in lattice models

Meurice¹

2012

Proceedings of the 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)

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Fisher zeros are the zeros of the partition function in the complex β = 2N c /g 2 plane. When they pinch the real axis, finite size scaling allows one to distinguish between first and second order transition and to estimate exponents. On the other hand, a gap signals confinement and the method can be used to explore the boundary of the conformal window. We present recent numerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge and SU(3) gauge theory with N f = 4 and 12 flavors. We discuss attempts to understand some of these results using analytical methods. We discuss the 2-lattice matching and qualitative aspects of the renormalization group (RG) flows in the Migdal-Kadanoff approximation, in particular how RG flows starting at large β seem to move around regions where bulk transitions occur. We consider the effects of the boundary conditions on the nonperturbative part of the average energy and on the Fisher zeros for the 1D O(2) model.

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Electromagnetic fluxes, monopoles, and the order of 4d compact U(1) phase transition

Cited by 43 publications

References 35 publications

U(1) lattice gauge theory with a topological action

U(1) lattice gauge theory with a topological action

Nonperturbative U(1) gauge theory at finite temperature

Fisher zeros and conformality in lattice models

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