The electron spin resonance spectrum of a quasi 1D S=1/2 antiferromagnet K2CuSO4Br2 was found to demonstrate an energy gap and a doublet of resonance lines in a wide temperature range between the Curie--Weiss and Ne`{e}l temperatures. This type of ma
gnetic resonance absorption corresponds well to the two-spinon continuum of excitations in S=1/2 antiferromagnetic spin chain with a uniform Dzyaloshinskii--Moriya interaction between the magnetic ions. A resonance mode of paramagnetic defects demonstrating strongly anisotropic behavior due to interaction with spinon excitations in the main matrix is also observed.
New features of the Mathematica code FIRE are presented. In particular, it can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated familie
s of Feynman integrals. As as an example, we consider four-loop massless propagator integrals for which LiteRed provides reduction rules and FIRE assists to apply these rules. So, as a by-product one obtains a four-loop variant of the well-known three-loop computer code MINCER. We also describe various ways to find additional relations between master integrals for several families of Feynman integrals.
For a fixed Feynman graph one can consider Feynman integrals with all possible powers of propagators and try to reduce them, by linear relations, to a finite subset of integrals, the so-called master integrals. Up to now, there are numerous examples
of reduction procedures resulting in a finite number of master integrals for various families of Feynman integrals. However, up to now it was just an empirical fact that the reduction procedure results in a finite number of irreducible integrals. It this paper we prove that the number of master integrals is always finite.
We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition im
plemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.
The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decomposition
s and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators and Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.
One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorit
hm is implemented as a Mathematica code MBresolve.m
The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over
loop momenta when possible. Currently it is being used in complicated three-loop calculations.
Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public lastyear by Bogner and Weinzierl. We present a new program performing the sector decomposition
and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral.
The entire magnetic phase diagram of the quasi two dimensional (2D) magnet on a distorted triangular lattice KFe(MoO4)2 is outlined by means of magnetization, specific heat, and neutron diffraction measurements. It is found that the spin network brea
ks down into two almost independent magnetic subsystems. One subsystem is a collinear antiferromagnet that shows a simple spin-flop behavior in applied fields. The other is a helimagnet that instead goes through a series of exotic commensurate-incommensurate phase transformations. In the various phases one observes either true 3D order or quasi-2D order. The experimental findings are compared to theoretical predictions found in literature
Spin resonance absorption of the triplet excitations is studied experimentally in the Haldane magnet PbNi2V2O8. The spectrum has features of spin S=1 resonance in a crystal field, with all three components, corresponding to transitions between spin s
ublevels, being observable. The resonance field is temperature dependent, indicating the renormalization of excitation spectrum in interaction between the triplets. Magnetic resonance frequencies and critical fields of the magnetization curve are consistent with a boson version of the macroscopic field theory [Affleck 1992, Farutin & Marchenko 2007], implying the field induced ordering at the critical field, while contradict the previously used approach of noninteracting spin chains.
