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Gernot Münster

Publications and source records attributed to Gernot Münster.

At least 55 records · Page 3Linked to original sources
arXiv2011

Twisted mass chiral perturbation theory for 2+1+1 quark flavours

We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to O(a^2). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, O(a)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.

hep-lat↗
arXiv2008

Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase

We perform euclidean strong coupling expansions for Yang Mills theory on the lattice at finite temperature. After setting up the formalism for general SU(N), we compute the first few terms of the series for the free energy density and the lowest screening mass in the case of SU(2). To next-to-leading order the free energy series agrees with that of an ideal gas of glueballs. This demonstrates that in the confined phase the quasi-particles indeed correspond to the T=0 hadron excitations, as commonly assumed in hadron resonance gas models. Our result also fixes the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method. In accord with Monte Carlo results, we find screening masses to be nearly temperature independent in the confined phase. This and the exponential smallness of the pressure can be understood as genuine strong coupling effects. Finally, we analyse Pade approximants to estimate the critical couplings of the phase transition, which for our short series are only ~25% accurate. However, up to these couplings the equation of state agrees quantitatively with numerical results on N_t=1-4 lattices.

hep-lat↗
arXiv2008

Interfacial roughening in field theory

In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with fluctuating, infinitely thin membranes, requiring ad hoc cut-offs in momentum space. We investigate the interface roughening from first principles in the framework of the Landau-Ginzburg model, that is renormalized field theory, in the one-loop approximation. The interface profile and width are calculated analytically, resulting in finite expressions with definite coefficients. They are valid in the scaling region and depend on the known renormalized coupling constant.

cond-mat.stat-mech↗
arXiv2007

The interfacial profile in two-loop order

The profile of interfaces separating different phases of statistical systems is investigated in the framework of renormalized field theory. The profile function is calculated analytically in the local potential approximation, using the effective potential to two loops. It can be interpreted as an intrinsic interfacial profile. The loop corrections to the leading tanh-type term turn out to be small. They yield a broadening of the interface.

cond-mat.stat-mech↗
arXiv2006

Twisted mass lattice QCD with non-degenerate quark masses

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term is considered in the framework of chiral perturbation theory. For two and three numbers of quark flavours, respectively, with non-degenerate quark masses the pseudoscalar meson masses and decay constants are calculated in next-to-leading order including lattice effects quadratic in the lattice spacing a.

hep-lat↗
arXiv2004

Profile and width of rough interfaces

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.

cond-mat.stat-mech↗
arXiv2004

Chiral perturbation theory for twisted mass QCD

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term for two degenerate quark flavours is considered in the framework of chiral perturbation theory. The pion masses and decay constants are calculated in next-to-leading order including terms linear in the lattice spacing a. We treat both unquenched and partially quenched QCD. We also discuss the phase structure of twisted mass lattice QCD.

hep-lat↗
arXiv2004

Chiral perturbation theory for partially quenched twisted mass lattice QCD

Partially quenched Quantum Chromodynamics with Wilson fermions on a lattice is considered in the framework of chiral perturbation theory. Two degenerate quark flavours are associated with a chirally twisted mass term. The pion masses and decay constants are calculated in next-to-leading order including terms linear in the lattice spacing $a$.

hep-lat↗
arXiv2004

On the phase structure of twisted mass lattice QCD

The introduction of a chirally twisted mass term has been proposed as an attractive approach to O(a) improvement of Quantum Chromodynamics with Wilson fermions on a lattice. For numerical simulation projects it is important to know the phase structure of the theory in the region of small quark masses. We study this question in the framework of chiral perturbation theory. Generalizing the analysis of Sharpe and Singleton we find extensions of normal and Aoki phase scenarios and a possible new phase with spontaneous breakdown of chiral symmetry to a discrete $Z_2$.

hep-lat↗
arXiv2004

Chiral perturbation theory for lattice QCD with a twisted mass term

Quantum Chromodynamics on a lattice with Wilson fermions and a chirally twisted mass term for two degenerate quark flavours is considered in the framework of chiral perturbation theory. The pion mass and decay constant are calculated in next-to-leading order including terms linear in the lattice spacing $a$.

hep-lat↗
arXiv2003

Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $ξ\to 0$ of the renormalizable R$_ξ$-gauge. We consider perturbation theory to one-loop order in the R$_ξ$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $ξ\to 0$ of the R$_ξ$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.

hep-th↗
arXiv2002

The classical nucleation rate in two dimensions

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. In homogeneous nucleation theory the nucleation rate $Γ$ can be written in the form of the Arrhenius law: $Γ=\mathcal{A} e^{-\mathcal{H}_{c}}$. Here $\mathcal{H}_{c}$ is the energy of the critical bubble, and the prefactor $\mathcal{A}$ can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. In general it is not possible to find explicit expressions for $\mathcal{A}$ and $\mathcal{H}_{c}$. If the difference $η$ between the energies of the stable and metastable vacua is small, the constant $\mathcal{A}$ can be determined within the leading approximation in $η$, which is an extension of the ``thin wall approximation''. We have done this calculation for the case of a model with a real-valued order parameter in two dimensions.

cond-mat.stat-mech↗
arXiv2001

Dynamical suppression of large instantons

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. We find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.

hep-lat↗
arXiv2000

On the 1-loop lattice perturbation theory of the supersymmetric Ward identities

The one loop corrections to the supersymmetric Ward identities (WIs) in the discretized N=1 SU(2) supersymmetric Yang-Mills theory can be investigated by means of lattice perturbation theory. The supersymmetry (SUSY) is explicitly broken by the lattice discretization as well as by the introduction of Wilson fermions. However, the renormalization of the supercurrent can be carried out in a scheme that restores the nominal continuum WIs. We present our work in progress which is concerned with the 1-loop renormalization of the local supercurrent, i.e. with the perturbative computation of the corresponding renormalization constants and mixing coefficients.

hep-lat↗
arXiv2000

Semiclassical calculation of the nucleation rate for first order phase transitions in the 2-dimensional phi^4-model beyond the thin wall approximation

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. Traditionally, this process is described by the semiclassical nucleation theory developed by Langer and, in the context of quantum field theory, by Callan and Coleman. They have shown that the nucleation rate $Γ$ can be written in the form of the Arrhenius law: $Γ=\mathcal{A}e^{-\mathcal{H}_{c}}$. Here $\mathcal{H}_{c}$ is the energy of the critical bubble, and the prefactor $\mathcal{A}$ can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. It is not possible to find explicit expressions for the constants $\mathcal{A}$ and $\mathcal{H}_{c}$ in the general case of a finite difference $η$ between the energies of the stable and metastable vacua. For small $η$, the constant $\mathcal{A}$ can be determined within the leading approximation in $η$, which is an extension of the ``thin wall approximation''. We have calculated the leading approximation of the prefactor for the case of a model with a real-valued order parameter field in two dimensions.

cond-mat.stat-mech↗
arXiv2000

Distribution of instanton sizes in a simplified instanton gas model

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. In one dimension exact results can be derived. In any dimension we find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.

hep-th↗
arXiv1999

Analytical Calculation of the Nucleation Rate for First Order Phase Transitions beyond the Thin Wall Approximation

First order phase transitions in general proceed via nucleation of bubbles. A theoretical basis for the calculation of the nucleation rate is given by the homogeneous nucleation theory of Langer and its field theoretical version of Callan and Coleman. We have calculated the nucleation rate beyond the thin wall approximation by expanding the bubble solution and the fluctuation determinant in powers of the asymmetry parameter. The result is expressed in terms of physical model parameters.

cond-mat.stat-mech↗