
Phase Transitions and Group Theory
F 2020 . 2021  1º semestre
Specification sheet Specific details
^{*)} N.B. if there are students who do not speak Portuguese the language is English.
Learning goals
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. 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. Prerequisites
Basic knowledge in Statistical Physics
Generic skills to reach
. Competence in analysis and synthesis;. Computer Skills for the scope of the study; . Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Competence in oral and written communication; . Creativity; . Competence in applying theoretical knowledge in practice; . Selfcriticism and selfevaluation; . Research skills; (by decreasing order of importance) Teaching hours per semester
Assessment
Bibliography of reference
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, AddisonWesley, 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). Teaching method
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. Resources used
