arXiv subjects

T. Reisz

Publications and source records attributed to T. Reisz.

At least 19 recordsLinked to original sources

arXiv2001

QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global Z_2 symmetry, two colourless boundstates, even and odd under Z_2, are identified. Their respective contributions (poles) in correlation functions of local composite operators A_n of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. No sizable signal in any A_n correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar ``matter'' fields confined within colourless boundstates whose residual ``strong'' interactions are very weak.

hep-lat↗

arXiv2000

Dynamical Linked Cluster Expansions for Spin Glasses

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. An associated graph theory with a generalized notion of connectivity is reviewed. We discuss physical applications to disordered systems, in particular to spin glasses, such as the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n=0, that usually goes along with an application of the replica trick.

cond-mat↗

arXiv2000

High Temperature 3D QCD: Dimensional Reduction at Work

We investigate the three-dimensional SU(3) gauge theory at finite temperature in the framework of dimensional reduction. The large scale properties of this theory are expected to be conceptually more complicated than in four dimensions. The dimensionally reduced action is computed in closed analytical form. The resulting effective two-dimensional theory is studied numerically both in the electric and magnetic sector. We find that dimensional reduction works excellently down to temperatures of 1.5 times the deconfinement phase transition temperature and even on rather short length scales. We obtain strong evidence that for ${\rm QCD}_3$, even at high temperature the colour averaged potential is represented by the exchange of a single state, at variance with the usual Debye screening picture involving a pair of electric gluons.

hep-lat↗

arXiv2000

Chiral symmetry restoration and axial vector renormalization for Wilson fermions

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.

hep-lat↗

arXiv1999

Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions

Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant under renormalization. This means that in the continuum limit the (standard) chiral symmetry becomes restored. In particular, the flavour mixing current does not require renormalization.

hep-lat↗

arXiv1999

Lattice QED and Universality of the Axial Anomaly

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem. The results generalize to non-abelian gauge theories.

hep-lat↗

arXiv1999

The axial anomaly in lattice QED. A universal point of view

hep-lat↗

arXiv1999

Analytical studies for the critical line and critical endpoint of the electroweak phase transition

We outline two approaches for studying the electroweak phase transition in the framework of the four-dimensional SU(2) Higgs model on a lattice. The first one is based on a combination of variational estimates for the free energy and a solution of the resulting gap equations by means of dynamical linked cluster expansions. In the second approach we first indicate the derivation of an effective scalar field theory upon integration over the gauge fields. The phase structure of the resulting scalar theory is then investigated by means of generalized linked cluster expansions. We present results for the critical line and the critical endpoint.

hep-lat↗

arXiv1998

Dynamical linke cluster expansions: Algorithmic aspects and applications

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline an associated multiple-line graph theory involving extended notions of connectivity and indicate an algorithmic implementation of graphs. Fields of applications are SU(N) gauge Higgs systems within variational estimates, spin glasses and partially annealed neural networks. We present results for the critical line in an SU(2) gauge Higgs model for the electroweak phase transition. The results agree well with corresponding high precision Monte Carlo results.

hep-lat↗

arXiv1998

Chiral symmetry restoration of QCD and the Gross-Neveu model

Two flavour massless QCD has a second order chiral transition which has been argued to belong to the universality class of the $3d$ O(4) spin model. The arguments have been questioned recently, and the transition was claimed to be mean field behaved. We discuss this issue at the example of the $3d$ Gross-Neveu model. A solution is obtained by applying various well established analytical methods.

hep-lat↗

arXiv1998

Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. We develop an associated graph theory with a generalized notion of connectivity and describe an algorithmic generation of the new multiple-line graphs. We indicate physical applications to spin glasses, partially annealed neural networks and SU(N) gauge Higgs systems. In particular the new expansion technique provides the possibility of avoiding the replica-trick in spin glasses. We consider variational estimates for the SU(2) Higgs model of the electroweak phase transition. The results for the transition line, obtained by dynamical linked cluster expansions, agree quite well with corresponding high precision Monte Carlo results.

hep-lat↗

arXiv1998

Hopping Parameter Series Construction for Models with Nontrivial Vacuum

Hopping parameter expansions are convergent power series. Under general conditions they allow for the quantitative investigation of phase transition and critical behaviour. The critical information is encoded in the high order coefficients. Recently, 20th order computations have become feasible and used for a large class of lattice field models both in finite and infinite volume. They have been applied to quantum spin models and field theories at finite temperature. The models considered are subject to a global ${\bf Z}_2$ symmetry or to an even larger symmetry group such as O(N) with $N\geq 2$. In this paper we are concerned with the technical details of series computations to allow for a nontrivial vacuum expectation value $<ρ(x)>\not=0$, which is typical for models that break a global ${\bf Z}_2$ symmetry. Examples are scalar fields coupled to an external field, or manifestly gauge invariant effective models of Higgs field condensates in the electroweak theory, even in the high temperature phase. A nonvanishing tadpole implies an enormous proliferation of graphs and limits the graphical series computation to the 10th order. To achieve the hopping parameter series to comparable order as in the ${\bf Z}_2$ symmetric case, the graphical expansion is replaced by an expansion into new algebraic objects called vertex structures. In this way the 18th order becomes feasible.

hep-lat↗

arXiv1998

The Monotony Criterion for A Finite Size Scaling Analysis of Phase Transitions

We propose a new criterion to analyse the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behaviour in volume for first and second order transitions close to the transition point. The criterion applies to analytical and numerical studies of phase diagrams including tricritical behaviour.

hep-lat↗

arXiv1997

The Gross-Neveu model and QCDs chiral phase transition

Quantum chromodynamics has a rather complicated phase structure. The finite temperature, chiral phase structure depends on the number of flavours and to a large extent on the particular values of the fermion masses. For two massless flavours there is a true second order transition. It has been argued that this transition belongs to the universality class of the three-dimensional O(4) spin model. The arguments have been questioned recently, and the transition was claimed to be mean field behaved. In this lecture we discuss this issue at the example of the three-dimensional, parity symmetric Gross-Neveu model at finite temperature, with a large number N of fermions. At zero temperature there is a phase where parity is spontaneously broken. At finite temperature, this model has a parity restoring second order transition. It reveals considerable similarity to the QCD chiral phase transition. There are related questions here concerning the universality class. We solve this problem essentially by means of the following methods: Large N expansion, dimensional reduction in the framework of quantum field theory, and high order convergent series expansions about disordered lattice systems.

hep-lat↗

arXiv1996

Linked Cluster Expansions on non-trivial topologies

Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result into convergent series for free energies, correlation functions and susceptibilities. The expansions have been generalized to field theories at finite temperature and to a finite volume. Detailed information on critical behaviour can be extracted from the high order behaviour of the susceptibility series. We outline some of the steps by which the 20th order is achieved.

hep-lat↗

arXiv1996

Finite Size Scaling Analysis with Linked Cluster Expansions

Linked cluster expansions are generalized from an infinite to a finite volume on a $d$-dimensional hypercubic lattice. They are performed to 20th order in the expansion parameter to investigate the phase structure of scalar $O(N)$ models for the cases of $N=1$ and $N=4$ in 3 dimensions. In particular we propose a new criterion to distinguish first from second order transitions via the volume dependence of response functions for couplings close to but not at the critical value. The criterion is applicable to Monte Carlo simulations as well. Here it is used to localize the tricritical line in a $Φ^4 + Φ^6$ theory. We indicate further applications to the electroweak transition.

hep-lat↗

arXiv1996

Linked cluster expansions beyond nearest neighbour interactions: convergence and graph classes

We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way that the classes of graphs to be considered are identical to those of the pure nearest neighbour interaction. The only change then concerns the computation of lattice imbedding numbers. All the complications that arise can be reduced to a generalization of the notion of free random walks, including hopping beyond nearest neighbour. Explicit expressions for combinatorical numbers of the latter are given. We show that under some general conditions the linked cluster expansion series have a non-vanishing radius of convergence.

hep-lat↗

arXiv1996

Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such as Monte Carlo simulations. Our computational tools are illustrated at the example of scalar O(N) models with four and six-point couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.

hep-lat↗