Renormalization group methods and the epistemology of effective field theories

The effective field theory (EFT) perspective on particle physics has yielded insight into the Standard Model. This paper investigates the epistemic consequences of the use of different variants of renormalization group (RG) methods as part of the EFT perspective on particle physics. RG methods are a family of formal techniques. While the semi-group variant of the RG has played a prominent role in condensed matter physics, the full-group variant has become the most widely applicable formalism in particle physics. We survey different construction techniques for EFTs in particle physics and analyze the role that semi-group and full-group variants of the RG play in each. We argue that the full-group variant is best suited to answering structural questions about relationships among EFTs at different scales, as well as explanatory questions, such as why the Standard Model has been empirically successful at low energy scales and why renormalizability was a successful criterion for constructing the Standard Model. We also present an account of EFTs in particle physics that is based on the full-RG. Our conclusion about the advantages of the full-RG is restricted to the particle physics case. We argue that a domain-specific approach to interpreting EFTs and RG methods is needed. Formal variations and flexibility in physical interpretation enable RG methods to support different explanatory strategies in condensed matter and particle physics. In particular, it is consistent to maintain that coarse-graining is an essential component of explanations in condensed matter physics, but not in particle physics.

Relevant Analytic Spontaneous Magnetization Relation for the Face-Centered-Cubic Ising Lattice

The relevant approximate spontaneous magnetization relations for the simple-cubic and body-centered-cubic Ising lattices have recently been obtained analytically by a novel approach that conflates the Callen-Suzuki identity with a heuristic odd-spin correlation magnetization relation. By exploiting this approach, we study an approximate analytic spontaneous magnetization expression for the face-centered-cubic Ising lattice. We report that the results of the analytic relation obtained in this work are nearly consistent with those derived from the Monte Carlo simulation.

An S-matrix approach to gravitational-wave physics

The detection of gravitational waves emitted by binary systems has opened a new astronomical window into the Universe. We describe recent advances in the field of scattering amplitudes applied to the post-Minkowskian expansion, and the extraction of the effective two-body gravitational potential. The techniques presented here apply to any effective field theory of gravity and are not restricted to four-dimensional Einstein gravity. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.

Higgs effect without lunch

Reduction in effective space-time dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wave function factors depend non-trivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a 'covert' pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. The Stueckelberg mode remains in the theory as a propagating scalar degree of freedom from a dimensionally reduced perspective, but it is not 'eaten' in a mass-generating mechanism. At leading order, it also makes no contribution to the conserved energy; for this reason, it may be called a (non-ghost) 'phantom'. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.

Phase diagram of the frustrated FCC antiferromagnet from effective-field theory

The phase diagram of a face-centred cubic (FCC) antiferromagnet is calculated from the effective field theory (EFT) of Honmura and Kaneyoshi taking into account not only the effect of interaction with nearest neighbours,J1, but also the effect of second neighbours,J2. The phase diagram for the nearest neighbour case away from the triple point, which in our calculations is predicted to be atH= 4 andT= 0, is close to cluster variation method (CVM) and Monte Carlo (MC) results. Similar to MC and CVM predictions, we observe that the increasing second neighbours interaction pushes the triple point towards zero field. Our calculations also show that forα= -J2/J1= 0.3, the triple point merges with the transition point of the L10phase, one of the ground states, atH= 0 and changes the nature of phase transition from first- to second-order, in full agreement with Monte Carlo predictions. The phase diagram with the effect of second neighbours calculated for several values ofαare in good agreement with available MC and CVM predictions.

Dynamics of Frenkel Excitons in Pentacene

The dispersion relation for noninteracting excitons and the influence of perturbative corrections are examined in the case of pentacene structure. The values of exchange integrals are determined by nonlinear fits to the experimental dispersion data, obtained by the inelastic electron scattering reported in recent experiments. We obtain theoretical dispersion curves along four different directions in the Brillouin zone which possess the same periodicity as the experimental data. We also show that perturbative corrections are negligible since the exciton gap in the dispersion relation is huge in comparison to the exchange integrals.

Tailoring Superconductivity with Quantum Dislocations

Despite the established knowledge that crystal dislocations can affect a material's superconducting properties, the exact mechanism of the electron-dislocation interaction in a dislocated superconductor has long been missing. Being a type of defect, dislocations are expected to decrease a material's superconducting transition temperature (T_c) by breaking the coherence. Yet experimentally, even in isotropic type I superconductors, dislocations can either decrease, increase, or have little influence on T_c. These experimental findings have yet to be understood. Although the anisotropic pairing in dirty superconductors has explained impurity-induced T_c reduction, no quantitative agreement has been reached in the case a dislocation given its complexity. In this study, by generalizing the one-dimensional quantized dislocation field to three dimensions, we reveal that there are indeed two distinct types of electron-dislocation interactions. Besides the usual electron-dislocation potential scattering, there is another interaction driving an effective attraction between electrons that is caused by dislons, which are quantized modes of a dislocation. The role of dislocations to superconductivity is thus clarified as the competition between the classical and quantum effects, showing excellent agreement with existing experimental data. In particular, the existence of both classical and quantum effects provides a plausible explanation for the illusive origin of dislocation-induced superconductivity in semiconducting PbS/PbTe superlattice nanostructures. A quantitative criterion has been derived, in which a dislocated superconductor with low elastic moduli and small electron effective mass and in a confined environment is inclined to enhance T_c. This provides a new pathway for engineering a material's superconducting properties by using dislocations as an additional degree of freedom.

Nonperturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and their capability of dealing with thermal transport phenomena for bulk material only. Here by utilizing a fully quantized dislocation field, which we called a "dislon", a phonon interacting with a dislocation is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime, which are reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. For instance, a renormalized phonon naturally resolves the decade-long debate between dynamic and static dislocation-phonon scattering approaches, as two limiting cases. In particular, at nanoscale, both the dynamic and static approaches break down, while the present renormalization approach remains valid by capturing the size effect, showing good agreement with lattice dynamics simulations.

Neutron Measurements and the Weak Nucleon-Nucleon Interaction

The weak interaction between nucleons remains one of the most poorly-understood sectors of the Standard Model. A quantitative description of this interaction is needed to understand weak interaction phenomena in atomic, nuclear, and hadronic systems. This paper summarizes briefly what is known about the weak nucleon-nucleon interaction, tries to place this phenomenon in the context of other studies of the weak and strong interactions, and outlines a set of measurements involving low energy neutrons which can lead to significant experimental progress.