Statistical Mechanics
A.Y. 2023/2024
Learning objectives
The main learning objective of the course is to provide a modern mathematical introduction to classical and quantistic statistical mechamics.
Expected learning outcomes
At the end of the course, students will be able to study, by means of modern mathematical tools, the main phenomena described by classical and quantistic statistical mechanics.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
First semester
Course syllabus
Phase transitions, criticl exponents and correlations. The Ising model.
Mean field and infinite range Ising model. Onsager solution
of the Ising model, multipolygon expansion, dimers, map in Grassmann integrals, critical exponents. Euclidean bosonic and fermionic path integrals. Phi4 models, Wick rule, linked cluster theorem, Feynman graphs expansion power counting. Exact Renormalization Group, multiscale decomposition, running coupling constants and Beta function. Vslidity of mean field in d>4, marginal irrelevance in d=4, triviality.
Esponenti critici e correlazioni. Modello di Ising. Campo Medio e Ising a portata infinita.
Soluzione di Onsager del modello di Ising,
espansione in multipoligoni, dimeri, mappa in integrale di Grassmann gaussiano, indici critici. Integrali euclidei bosonici e di Grassmann.
Modelli phi4, regola di Wick,
teorema linked-cluster, espansione in grafici di Feynman, conteggo di potenze.
Gruppo di Rinormalizzazione esatto, decomposizione multiscala, costanti correnti e funzione beta.
Validita' campo medio in d maggiore di 4, rinormalizzazione Tc,
irrilevanza marginale in d=4 e trivialita'
Mean field and infinite range Ising model. Onsager solution
of the Ising model, multipolygon expansion, dimers, map in Grassmann integrals, critical exponents. Euclidean bosonic and fermionic path integrals. Phi4 models, Wick rule, linked cluster theorem, Feynman graphs expansion power counting. Exact Renormalization Group, multiscale decomposition, running coupling constants and Beta function. Vslidity of mean field in d>4, marginal irrelevance in d=4, triviality.
Esponenti critici e correlazioni. Modello di Ising. Campo Medio e Ising a portata infinita.
Soluzione di Onsager del modello di Ising,
espansione in multipoligoni, dimeri, mappa in integrale di Grassmann gaussiano, indici critici. Integrali euclidei bosonici e di Grassmann.
Modelli phi4, regola di Wick,
teorema linked-cluster, espansione in grafici di Feynman, conteggo di potenze.
Gruppo di Rinormalizzazione esatto, decomposizione multiscala, costanti correnti e funzione beta.
Validita' campo medio in d maggiore di 4, rinormalizzazione Tc,
irrilevanza marginale in d=4 e trivialita'
Prerequisites for admission
Nozioni di base
Teaching methods
In person lectures
Teaching Resources
Mastropietro Dispense
Zinn-Justin Quantum Field Theory and Critical Phenomena: Oxford un. Press
C. Itzykson, J. Drouffe Statistical Field Theory, Cambridge Un. Press 1991
G. Parisi Statistical Field Theory
Fradkin Field Theories of condensed matter physics Cambridge Un. Press 1991
Zinn-Justin Quantum Field Theory and Critical Phenomena: Oxford un. Press
C. Itzykson, J. Drouffe Statistical Field Theory, Cambridge Un. Press 1991
G. Parisi Statistical Field Theory
Fradkin Field Theories of condensed matter physics Cambridge Un. Press 1991
Assessment methods and Criteria
Written and oral exam
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Mastropietro Vieri
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