Phase Transitions and Group Theory

Recommended Prerequisites

Basic knowledge in Statistical Physics.

Teaching Methods

Some topics are addressed in lectures, others are proposed to the students as problems to solve individually at home, after a short introduction in lectures that will be presented by the students, and discussed in the tutorials.

Concerning group theory, emphasis will be given to applications in different field of Physics: Condensed Matter Physics, Particle Physics, etc.

Learning Outcomes

Main learning outcomes:

Deep knowledge of the statistical mechanics and group theory methods, including applications;

Characterisation of the different types of phase transitions, critical exponents, universality classes, etc.

Theoretical understanding of the physical phenomena involved in phase transitions.

Autonomous problem solving by the students, using the mathematical tools taught in the syllabus, within this field.

Other learning outcomes:

Capacity to search relevant literature to address a specific problem. To be acquainted with the current research being done in this field.

Work Placement(s)

No

Syllabus

Free energy and statistical ensembles (revision).
Quantum statistics (revision).
Order parameters; symmetry breaking; topology.
Landau's theory of phase transitions.
Correlations, response and dissipations.
Abrupt (1st order) and continuous (2nd order) phase transitions.
Symmetries (basic concepts).
Groups; representation of groups.
Irreducible representations; properties of vector and tensor irreducible operators.
Applications of group theory.
Continuous groups.

Head Lecturer(s)

João Pedro Trancoso Gomes Rosa

Assessment Methods

Assessment
Resolution Problems: 30.0%
Exam: 70.0%

Bibliography

K. HUANG, Statistical Mechanincs, Wiley & Sons, 1987.
L. E. REICHL, A modern course in statistical physics, Univ. of Texas, 1980.
N. GOLDENFELD, Lectures on phase transitions and the renormalization group, Addison-Wesley, 1992.
J. M. YEOMANS, Statistical Mechanics of phase transitions, Claredon Press, 1992.
M. TINKHAM, Group Theory and Quantum Mechanics, Dover (2003)
R. McWEENY, Symmetry: an introduction to group theory and its applications, Dover (1963).