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Lecture# Scaling of Free Energy

Description

This lecture covers the scaling of free energy and correlation length, discussing the Renormalization Group flow in Quantum Field Theory, relevant and irrelevant scaling variables, and the critical surface codimension. It also explores the Ising model, critical exponents, and scaling relations based on the number of relevant scaling variables.

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In course

Instructors (2)

PHYS-739: Conformal Field theory and Gravity

This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.

Related concepts (24)

Renormalization group

In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation.

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

History of quantum field theory

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature.

Scalar field theory

In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.

Scale invariance

In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. In mathematics, scale invariance usually refers to an invariance of individual functions or curves.

Related lectures (19)

Renormalization Group in Field TheoryPHYS-739: Conformal Field theory and Gravity

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Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Scaling & Renormalization in Statistical MechanicsPHYS-739: Conformal Field theory and Gravity

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Statistical Field TheoryPHYS-316: Statistical physics II

Covers the basics of statistical field theory, focusing on Ising models and the Ginsburg-Landau theory.

Conformal Field Theories: Review and ScalingPHYS-739: Conformal Field theory and Gravity

Covers statistical mechanics, conformal field theories, and critical exponents, emphasizing the importance of universality and renormalization group flows.