Phase structure of Abelian Higgs model on a lattice: an analytical analysis

Yang, Jin Min; Wu, Chi-min; Zhao, Pei Ying

doi:10.1088/0954-3899/18/1/001

J. Phys. G: Nucl. Part. Phys.

1992

DOI: 10.1088/0954-3899/18/1/001

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Phase structure of Abelian Higgs model on a lattice: an analytical analysis

Jin Min Yang

Chi-min Wu

Pei Ying Zhao

Abstract: The variational cumulant expansion is extended to d-dimensional U(]) gauge .theory with radially active Higgs fields in the fundamental representation. The phase structures are given for d = 3 and d = 4 cases. A comparison with Monte Carlo and mean field results is also presented.

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“…Examples of these methods have appeared under many names, including optimised pertubation theory[4], action-variational approach [17], variational perturbation theory [21], method of self-similar approximations [22], screened perturbation theory [20],and the variational cumulant expansion [23]. The method has been applied successfully to 1 the evaluation of simple integrals [5,14,15], solving non-linear differential equations [16], quantum mechanics [5,13,24,25,26], cosmological slow roll transitions [7] and to quantum field theory, both in the continuum [26,21] and on the lattice [5,8,9,10,11,12,17,18,19,23,28,29]. Since the LDE approach is analytical, we do not have to worry about the presence of a complex action.…”

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Non-perturbative calculations of a global theory at finite density and temperature

2001

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We use an optimised hopping parameter expansion for the free energy (linear δ-expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero chemical potential becomes first order as the chemical potential increases. * email: T.Evans@ic.ac.uk , WWW: http://theory.ic.ac.uk/~time † Having ruled out a perturbative approach we turn to the various available nonperturbative techniques. One's first thought is to use Monte Carlo (MC) techniques to tackle the problem. However, MC methods usually fail when considering models at finite densities. This is because the Euclidean action, which is used as a statistical weight for the system, becomes complex, making a simple statistical integration technique imposible.To replace the MC approach we need an analytical non-perturbative method. The method chosen in this paper is an example of a general family sometimes called linear δ-expansions [5]. Examples of these methods have appeared under many names, including optimised pertubation theory[4], action-variational approach [17], variational perturbation theory [21], method of self-similar approximations [22], screened perturbation theory [20],and the variational cumulant expansion [23]. The method has been applied successfully to 1 the evaluation of simple integrals [5,14,15], solving non-linear differential equations [16], quantum mechanics [5,13,24,25,26], cosmological slow roll transitions [7] and to quantum field theory, both in the continuum [26,21] and on the lattice [5,8,9,10,11,12,17,18,19,23,28,29]. Since the LDE approach is analytical, we do not have to worry about the presence of a complex action. The expectation value of all physical observables will turn out to be real.The work in this paper with the U(1) or O(2) model builds on that set out in [4] for the case of zero temperature and zero chemical potential. However, here we phrase the model in terms of the field and its conjugate (Φ, Φ * ) rather than working with the real components of the field. This change is made because the charge operator is diagonal in this representation and so much easier to deal with [32].This paper is also complementary to the work done on the U(1) model using LDE methods in the continuum at finite temperature and finite chemical potential [6]. The Linear Delta expansionThe general format of the LDE method is to take a given expansion, whether it be a perturbative expansion in the continuum or a cumulant expansion on the lattice, and to provide an order by order optimisation of this expansion. It is in this process of optimisation that non-perturbative information emerges. It is straightforward, in principle, to expand beyond leading order, unlike other non-perturbative methods like large-N expansions or mean-field approximations.The first step in the method is to replace the physical ac...

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Non-perturbative calculations of a global theory at finite density and temperature

2001

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An optimized perturbation expansion for a global O(2) theory

2000

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On the phase structure of the 3D SU(2)-Higgs model and the electroweak phase transition

Evans¹,

Jones²,

Ritz³

1998

Nuclear Physics B

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The phase structure of the 3D SU (2)-Higgs model, the dimensionally reduced effective theory for the electroweak model at finite temperature, is analysed on the lattice using a variant of the linear δ-expansion. We develop a systematic variational cumulant expansion for general application to the study of gauge invariant operators in 3D gauge-Higgs models, with emphasis on the symmetric phase. In particular, the technique is not restricted to finite lattice volumes, and application to the fundamental 3D SU (2)-Higgs model allows the discontinuity of certain observables across the first-order transition to be observed directly for small 4D Higgs masses. The resulting phase structure agrees well with Monte Carlo simulations for small Higgs masses, but, at least to the order calculated, the technique is less sensitive to the expected evolution of the transition to a crossover for Higgs masses above 80 GeV.

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Phase structure of Abelian Higgs model on a lattice: an analytical analysis

Abstract: The variational cumulant expansion is extended to d-dimensional U(]) gauge .theory with radially active Higgs fields in the fundamental representation. The phase structures are given for d = 3 and d = 4 cases. A comparison with Monte Carlo and mean field results is also presented.

Cited by 3 publications

References 22 publications

Non-perturbative calculations of a global theory at finite density and temperature

Non-perturbative calculations of a global theory at finite density and temperature

An optimized perturbation expansion for a global O(2) theory

On the phase structure of the 3D SU(2)-Higgs model and the electroweak phase transition

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