Magnetic Catalysis: A Review (1207.5081v2)

Abstract: We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.

• The paper demonstrates that external magnetic fields induce dimensional reduction, enhancing fermion pairing and catalyzing mass generation.
• The paper compares theoretical models like NJL and quark-meson frameworks to validate the universal nature of magnetic catalysis.
• The paper highlights implications in QED, QCD, and graphene, suggesting potential experimental applications and new research directions.

Review of "Magnetic Catalysis: A Review" by Igor A. Shovkovy

The paper "Magnetic Catalysis: A Review" by Igor A. Shovkovy provides a comprehensive assessment of the magnetic catalysis phenomenon, a process characterized by the enhancement of dynamical symmetry breaking due to the presence of an external magnetic field. This review explores the dimensional reduction as a core theoretical framework to explain how magnetic fields influence fermion pairing dynamics, resulting in mass generation and symmetry breaking. The phenomenon has far-reaching implications across various fields, including particle physics, condensed matter systems, cosmology, and nuclear physics.

Theoretical Foundation and Dimensional Reduction

Magnetic catalysis asserts itself as a universal and model-independent phenomenon. At its core lies the dimensional reduction of fermionic systems in a magnetic field, leading to enhanced formation of spin-zero fermion-antifermion condensates. These condensates correlate with the breaking of global symmetries, significant in contexts such as chiral symmetry in quantum chromodynamics (QCD) and spin-valley symmetry in materials like graphene. Notably, the field's role contrasts with its effect in superconductivity through its potential to stabilize chiral condensates as opposed to destabilizing Cooper pairs.

The mechanistic interpretation involves the reduction of dimensions, D → D-2, effectively changing the dynamics of fermion pairing processes. This dimensional reduction implies the emergence of bound states from virtually no potential, realized in scenarios varying from weak coupling limits to nonperturbative domains. Magnetic fields provide an additional degree of control, allowing for the tuning of mass generation.

Historical Context and Model Applicability

The origins of magnetic catalysis trace back to the discovery that strong magnetic fields stabilize chirally broken vacuum states. This effect was first articulated in models with local four-fermion interactions in various dimensions. The uniformity of the phenomenon across different dimensions indicates its robust, model-independent nature. The corresponding dynamics have been validated in numerous theoretical frameworks, including Nambu-Jona-Lasinio (NJL) models, quark-meson models, and within chiral perturbation theory, among others.

Case Studies: Applications in QED, QCD, and Graphene

1. QED and QCD: The interaction of magnetic catalysis with gauge theories such as Quantum Electrodynamics (QED) and QCD is critically examined. In QED, the magnetic catalysis mechanism significantly lowers the energy for bound states, catalyzing symmetry breaking via nonperturbative dynamics in weakly coupled settings. Furthermore, in QCD, the interplay with the strong interaction, specifically in the presence of a strong magnetic field, suggests modifications to gluon dynamics and influence over chiral phase structures. The effect on QCD is evident from changes in dynamical quark masses and transformation of vacuum properties.
2. Graphene: Graphene serves as a quintessential example in condensed matter physics for analyzing magnetic catalysis under the quantum Hall effect. Because of graphene's band structure and the emergence of Dirac fermions, magnetic catalysis aids in understanding the transition leading to insulating behavior at the Dirac points. The theoretical underpinnings regarding the dynamical generation of Dirac and Haldane masses in graphene elucidate potential areas for experimental exploration in materials science.

Implications and Future Directions

The theoretical and practical ramifications of magnetic catalysis are profound, offering pathways to control and fine-tune the behavior of quantum systems under magnetic influence. Such a control could have implications in the development of advanced materials, experimental precision in particle colliders, and novel insights into condensed matter systems. Future research efforts may focus on precise interactions within environments with competing dynamics, such as temperature variations and external field gradients, potentially uncovering new physical regimes or states.

In conclusion, "Magnetic Catalysis: A Review" fortifies our understanding of how magnetic fields can induce and control dynamical processes in various theoretical and physical contexts. As research progresses, the opportunity to apply these concepts in new domains continues to expand, paving the way for innovative technological applications and deeper insights into the subtleties of symmetry and mass generation.