Here are my draft abstracts and keywords for the whole book and for chapters 6-10. Context and chapters 1-5 were given in the previous post.

Comments and suggestions are welcome.

*Condensed Matter Physics: A Very Short Introduction*

There are many more states of matter than just solid, liquid, and gas. Examples include liquid crystal, ferromagnet, glass, superfluid, and superconductor. New states are continually, and unexpectedly, being discovered. A superconductor can be like Schrodinger’s cat and in the macroscopic world exhibit the weirdness associated with the microscopic world of atoms, photons, and electrons, that is described by quantum theory. Condensed matter physics investigates how states of matter, and their distinct physical properties emerge from the atoms that a material is composed of. Such a system composed of many interacting parts can have properties that the parts do not have. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena are central to condensed matter physics and occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. When do quantitative differences become qualitative differences? Can simple models describe rich and complex behaviour? What is the relationship between the particular and the universal? How is the abstract related to the concrete? *Condensed Matter Physics: A Very Short Introduction* is concerned with such big questions. The materials in silicon chips, liquid crystal displays, and magnetic computer memories, may have transformed society. But, understanding them has transformed how we think about complex systems. Key concepts explored include phase diagrams, phase transitions, symmetry, types of order, spontaneous symmetry breaking, spatial dimensionality, scaling, universality, macroscopic quantum states, topology, metrology, and emergence.

Keywords: condensed matter physics, states of matter, phase transition, broken symmetry, emergence, solid-state physics, superconductivity, Physics Nobel Prize, theoretical physics, metrology

**Chapter 6. The critical point**

“The critical point” in a phase diagram denotes the conditions under which a continuous transition between two states of matter occurs. Surprisingly, near the critical point diverse systems can have the same dependence of physical properties on parameters such as temperature is the same. The only details that determine the critical exponents are the symmetry of the order parameter and the spatial dimensionality of the system. This independence from chemical and structural details, known as universality, presented a major challenge to theoretical physics for decades. Theory must deal with the large fluctuations in the amount of order that occurs close the critical point. The successful theory developed in the 1970s exploits the fact that different states of a system and different systems can be related to one another by mathematically rescaling the length scales in the system. The mathematics can be made tractable by consider the abstract idea of a system with variable number of spatial dimensions. The idea of rescaling is illustrated with the results of computer simulations of an Ising model and with images of fractals.

Keywords: Critical point, phase diagram, phase transition, critical exponent, universality, Ken Wilson, renormalisation group, scaling, fractals

**7. Quantum matter**

“Quantum matter” describes how some states of matter, such as superconductors and superfluids, have properties like those found in the strange quantum world of atoms, electrons, and photons. In quantum theory, properties such as energy cannot have any possible value, but are quantised. That is they come in discrete lumps. Also, particles can act like waves and so interfere with themselves. The weirdness of quantum theory is captured in the paradox of Schrödinger’s cat, where quantum effects occur on the macroscopic scale. This is realised in a superconductor, where the magnetic flux is quantised. Josephson proposed an electrical circuit that is the basis for a Superconducting Quantum Interference Device (SQUID). These devices are of technological significance as they are used in quantum computing, and to make precise measurements of fundamental physical constants and of magnetic field strengths. SQUIDs are now used in metrology, the science of precise measurements, being the basis for the international standard for the Volt, the unit of electrical voltage, and are used in quantum computing.

Keywords: Schrödinger’s cat, quantum theory, Josephson effect, SQUID, superconductor, superfluid, metrology, magnetic flux, macroscopic quantum effect, quantum computing

**8. Topology matters**

“Topology matters” in condensed matter physics because topology provides a means to describe the unusual types of order found in some states of matter in which there is no symmetry breaking. Topology is the field of mathematics covering the properties of geometric objects that do not change when smoothly deformed. The Hall effect is the existence of a new type of electrical resistance in a conductor caused by an electric current moving transverse to a magnetic field. In a two-dimensional metal (Flatland) in a large magnetic field, the Hall resistance is quantised in units defined by fundamental constants. This is a macroscopic quantum effect and provides a means to make highly precise measurements of electrical resistance. This quantum Hall effect is now used in metrology, being the basis for the international standard for the ohm, the unit of electrical resistance. Topology helps explain why the Hall resistance is so precisely quantised and is independent of so many details such as the chemical composition of the material in which the electrons move. Haldane showed that topology is also key to understanding the unusual properties of chains of magnetic atoms. They exhibit new states of matter, quite distinct from those found in three-dimensional magnets. Haldane also laid the foundation for proposals of topological insulators, a state of matter which is an electrical conductor on its surfaces, but an insulator in its interior.

Keywords: Topology, quantum Hall effect, mathematics, topological invariant, metrology, Duncan Haldane, topological insulator, Flatland

**9. Emergence: more is different**

“Emergence: more is different” discusses how the concept of emergence is central to condensed matter physics. An emergent property of a system composed of many interacting parts is a property that the individual parts do not have. The whole is greater than the sum of the parts. Other characteristics of emergent properties such as irreducibility, universality, and unpredictability are discussed. Emergent properties are illustrated with an example involving language, grammar, and literature. States of matter are emergent, as are the quasiparticles present in many systems. Phil Anderson argued that a hierarchy of scales illuminates the relationship between different scientific disciplines and shows the limitations of reductionism. Emergence explains why condensed matter physics works as a unified discipline. Due to universality, there are concepts and theories that describe phenomena in a wide range of materials. An emergence perspective highlights how discerning the relevant scale is central to effective scientific strategies aiming to understand complex systems, whether in physics, biology, or sociology.

Keywords: Emergence, reductionism, condensed matter physics, universality, philosophy of science, Phil Anderson, biology, stratification, quasiparticles, complex systems

**10. An endless frontier**

“An endless frontier” discusses how is difficult to predict the future of condensed matter physics, but it is likely to be an exciting one as new discoveries of emergent phenomena, such as novel states of matter, are often not anticipated. Grand challenges are identified including understanding glasses, Schrödinger’s cat, and exploring new materials, and new extremes of temperature, pressure, and magnetic field. Condensed matter physics has a rich history of contributing concepts, techniques, and personnel to other fields, including chemistry, biology, computer science, and materials engineering. This interdisciplinarity is likely to continue with investigations of complex systems, soft matter, and the social sciences. New technologies will aid new discoveries in condensed matter physics and vice versa. Threats to the future vitality of the field are like those for other intellectual enterprises imbedded in institutions increasingly controlled by financial values: a preoccupation with short-term commercial outcomes, hype, metrics, and managerialism. Advances have historically come from individuals and groups working within contexts and institutions that valued intellectual freedom, creativity, patience, curiousity, and serendipity.

Keywords: condensed matter physics, glass, complexity, emergence, science funding, hype, scientific discovery, materials science, interdisciplinarity

Any suggestions for improvement?