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F. Niedermayer

Publications and source records attributed to F. Niedermayer.

At least 19 recordsLinked to original sources
arXiv2019

On the rotator Hamiltonian for the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime

We investigate some properties of the standard rotator approximation of the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $\ell=L_t/L\to\infty\,.$ The difference between the results involves terms vanishing like $1/\ell\,,$ plus terms vanishing exponentially with $\ell\,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3\,.$

hep-th↗
arXiv2016

Finite-size corrections to scaling of the magnetization distribution in the $2d$ $XY$-model at zero temperature

The zero-temperature, classical $XY$-model on an $L \times L$ square-lattice is studied by exploring the distribution $Φ_L(y)$ of its centered and normalized magnetization $y$ in the large $L$ limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of $Φ_L(y)$, and the limit distribution $Φ_{L \rightarrow \infty} (y) = Φ_0(y)$ is obtained with high precision. The two leading finite-size corrections $Φ_L (y) -Φ_0 (y) \approx a_1(L)\, Φ_1(y) + a_2(L)\,Φ_2(y)$ are also extracted both from numerics and from analytic calculations. We find that the amplitude $a_1(L)$ scales as $\ln(L/L_0) /L^2$ and the shape correction function $Φ_1 (y)$ can be expressed through the low-order derivatives of the limit distribution, $Φ_1 (y) = [\,y\, Φ_0 (y) + Φ'_0 (y)\,]'$. The second finite-size correction has an amplitude $a_2(L)\propto 1/L^2$ and one finds that $a_2\,Φ_2(y) \ll a_1 \,Φ_1(y)$ already for small system size ($L> 10$). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the $XY$-model at low temperatures, including $T = 0$.

cond-mat.stat-mech↗
arXiv2012

Topological Lattice Actions for the 2d XY Model

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition - at least up to moderate vortex suppression. Thus our study underscores the robustness of universality, which persists even when basic principles of classical physics are violated. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. In the massless phase, the BKT value of the critical exponent eta_c is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

hep-lat↗
arXiv2012

Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models

We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.

hep-lat↗
arXiv2009

2+1 Flavor QCD simulated in the epsilon-regime in different topological sectors

We generated configurations with the parametrized fixed-point Dirac operator D_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the distributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2 topological sectors with that of the Random Matrix Theory predictions. The ratios of expectation values of the lowest eigenvalues and the cumulative eigenvalue distributions are studied for all combinations of k and nu. After including the finite size correction from one-loop chiral perturbation theory we obtained for the chiral condensate in the MSbar scheme Sigma(2GeV)^{1/3}=0.239(11) GeV, where the error is statistical only.

hep-lat↗
arXiv2006

Does the XY Model have an integrable continuum limit?

The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.

hep-lat↗
arXiv2006

Repairing Stevenson's step in the 4d Ising model

In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved statistics and show that the results are indeed consistent with conventional wisdom once one takes into account the uncertainty of lattice artifacts in the analytical computations.

hep-lat↗
arXiv2004

The Quenched Continuum Limit

We show that all current formalisms for quarks in lattice QCD are consistent in the quenched continuum limit, as they should be. We improve on previous extrapolations to this limit, and the understanding of lattice systematic errors there, by using a constrained fit including both leading and sub-leading dependence on a.

hep-lat↗
arXiv2002

Testing the fixed-point QCD action and the construction of chiral currents

We present the first set of quenched QCD measurements using the recently parametrized fixed-point Dirac operator D^FP. We also give a general and practical construction of covariant densities and conserved currents for chiral lattice actions. The measurements include (a) hadron spectroscopy, (b) corrections of small chiral deviations, (c) the renormalized quark condensate from finite-size scaling and, independently, spectroscopy, (d) the topological susceptibility, (e) small eigenvalue distributions and random matrix theory, and (f) local chirality of near-zero modes and instanton-dominance.

hep-lat↗
arXiv2001

First results from a parametrized Fixed-Point QCD action

We have constructed a new fermion action which is an approximation to the (chirally symmetric) Fixed-Point action, containing the full Clifford algebra with couplings inside a hypercube and paths built from renormalization group inspired fat links. We present an exploratory study of the light hadron spectrum and the energy-momentum dispersion relation.

hep-lat↗
arXiv2001

Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents

In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D^FP, see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Sigma and the topological susceptibility chi_t, and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions.

hep-lat↗
arXiv2000

Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action

We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all required symmetries. Optimizing a specific construction with hypercubic fermion offsets, we present some preliminary results.

hep-lat↗
arXiv2000

Asymptotically free theories based on discrete subgroups

We study the critical behavior of discrete spin models related to the 2d O(3) non-linear sigma model. Precise numerical results suggest that models with sufficiently large discrete subgroups are in the same universality class as the original sigma model. We observe that at least up to correlation lengths $ξ\approx 300$ the cut-off effects follow effectively an $\propto a$ behaviour both in the O(3) and in the dodecahedron model.

hep-lat↗
arXiv2000

The construction of generalized Dirac operators on the lattice

We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.

hep-lat↗
arXiv2000

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.

hep-th↗
arXiv1996

Improved lattice actions

The main strategies to reduce lattice artifacts for spin models, gauge fields, free fermions and QCD are discussed.

hep-lat↗
arXiv1995

Fixed point actions for SU(3) gauge theory

We summarize our recent work on the construction and properties of fixed point (FP) actions for lattice $SU(3)$ pure gauge theory. These actions have scale invariant instanton solutions and their spectrum is exact through 1--loop, i.e. in their physical predictions there are no $a^n$ nor $g^2 a^n$ cut--off effects for any $n$. We present a few-parameter approximation to a classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity $G = L \sqrt{σ(L)}$, where the string tension $σ(L)$ is measured from the torelon mass $μ= L σ(L)$, on lattices of fixed physical volume and varying lattice spacing $a$. While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for $ 1/2 \ge aT_c$.

hep-lat↗