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Phase transitions and renormalisation group [[electronic resource] /] / Jean Zinn-Justin
Phase transitions and renormalisation group [[electronic resource] /] / Jean Zinn-Justin
Autore Zinn-Justin Jean
Pubbl/distr/stampa Oxford, : Oxford University Press, 2007
Descrizione fisica 1 online resource (465 p.)
Disciplina 530.414
Collana Oxford graduate texts
Soggetto topico Phase transformations (Statistical physics)
Renormalization (Physics)
Soggetto genere / forma Electronic books.
ISBN 0-19-966516-8
1-281-15003-7
1-4356-2187-5
0-19-152774-2
9786611150037
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; 1 Quantum field theory and the renormalization group; 1.1 Quantum electrodynamics: A quantum field theory; 1.2 Quantum electrodynamics: The problem of infinities; 1.3 Renormalization; 1.4 Quantum field theory and the renormalization group; 1.5 A triumph of QFT: The Standard Model; 1.6 Critical phenomena: Other infinities; 1.7 Kadanoff and Wilson's renormalization group; 1.8 Effective quantum field theories; 2 Gaussian expectation values. Steepest descent method; 2.1 Generating functions; 2.2 Gaussian expectation values. Wick's theorem
2.3 Perturbed Gaussian measure. Connected contributions2.4 Feynman diagrams. Connected contributions; 2.5 Expectation values. Generating function. Cumulants; 2.6 Steepest descent method; 2.7 Steepest descent method: Several variables, generating functions; Exercises; 3 Universality and the continuum limit; 3.1 Central limit theorem of probabilities; 3.2 Universality and fixed points of transformations; 3.3 Random walk and Brownian motion; 3.4 Random walk: Additional remarks; 3.5 Brownian motion and path integrals; Exercises; 4 Classical statistical physics: One dimension
4.1 Nearest-neighbour interactions. Transfer matrix4.2 Correlation functions; 4.3 Thermodynamic limit; 4.4 Connected functions and cluster properties; 4.5 Statistical models: Simple examples; 4.6 The Gaussian model; 4.7 Gaussian model: The continuum limit; 4.8 More general models: The continuum limit; Exercises; 5 Continuum limit and path integrals; 5.1 Gaussian path integrals; 5.2 Gaussian correlations. Wick's theorem; 5.3 Perturbed Gaussian measure; 5.4 Perturbative calculations: Examples; Exercises; 6 Ferromagnetic systems. Correlation functions; 6.1 Ferromagnetic systems: Definition
6.2 Correlation functions. Fourier representation6.3 Legendre transformation and vertex functions; 6.4 Legendre transformation and steepest descent method; 6.5 Two- and four-point vertex functions; Exercises; 7 Phase transitions: Generalities and examples; 7.1 Infinite temperature or independent spins; 7.2 Phase transitions in infinite dimension; 7.3 Universality in infinite space dimension; 7.4 Transformations, fixed points and universality; 7.5 Finite-range interactions in finite dimension; 7.6 Ising model: Transfer matrix; 7.7 Continuous symmetries and transfer matrix
7.8 Continuous symmetries and Goldstone modesExercises; 8 Quasi-Gaussian approximation: Universality, critical dimension; 8.1 Short-range two-spin interactions; 8.2 The Gaussian model: Two-point function; 8.3 Gaussian model and random walk; 8.4 Gaussian model and field integral; 8.5 Quasi-Gaussian approximation; 8.6 The two-point function: Universality; 8.7 Quasi-Gaussian approximation and Landau's theory; 8.8 Continuous symmetries and Goldstone modes; 8.9 Corrections to the quasi-Gaussian approximation; 8.10 Mean-field approximation and corrections; 8.11 Tricritical points; Exercises
9 Renormalization group: General formulation
Record Nr. UNINA-9910465152403321
Zinn-Justin Jean  
Oxford, : Oxford University Press, 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Phase transitions and renormalisation group [[electronic resource] /] / Jean Zinn-Justin
Phase transitions and renormalisation group [[electronic resource] /] / Jean Zinn-Justin
Autore Zinn-Justin Jean
Pubbl/distr/stampa Oxford, : Oxford University Press, 2007
Descrizione fisica xii, 452 p
Disciplina 530.414
Collana Oxford graduate texts
Soggetto topico Phase transformations (Statistical physics)
Renormalization (Physics)
ISBN 0191527742
9780191527746
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910795728003321
Zinn-Justin Jean  
Oxford, : Oxford University Press, 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Phase transitions and renormalization group / / Jean Zinn-Justin
Phase transitions and renormalization group / / Jean Zinn-Justin
Autore Zinn-Justin Jean
Edizione [1st ed.]
Pubbl/distr/stampa Oxford, : Oxford University Press, 2007
Descrizione fisica xii, 452 p
Disciplina 530.414
Collana Oxford graduate texts
Soggetto topico Phase transformations (Statistical physics)
Renormalization (Physics)
ISBN 0191527742
9780191527746
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Contents -- 1 Quantum field theory and the renormalization group -- 1.1 Quantum electrodynamics: A quantum field theory -- 1.2 Quantum electrodynamics: The problem of infinities -- 1.3 Renormalization -- 1.4 Quantum field theory and the renormalization group -- 1.5 A triumph of QFT: The Standard Model -- 1.6 Critical phenomena: Other infinities -- 1.7 Kadanoff and Wilson's renormalization group -- 1.8 Effective quantum field theories -- 2 Gaussian expectation values. Steepest descent method -- 2.1 Generating functions -- 2.2 Gaussian expectation values. Wick's theorem -- 2.3 Perturbed Gaussian measure. Connected contributions -- 2.4 Feynman diagrams. Connected contributions -- 2.5 Expectation values. Generating function. Cumulants -- 2.6 Steepest descent method -- 2.7 Steepest descent method: Several variables, generating functions -- Exercises -- 3 Universality and the continuum limit -- 3.1 Central limit theorem of probabilities -- 3.2 Universality and fixed points of transformations -- 3.3 Random walk and Brownian motion -- 3.4 Random walk: Additional remarks -- 3.5 Brownian motion and path integrals -- Exercises -- 4 Classical statistical physics: One dimension -- 4.1 Nearest-neighbour interactions. Transfer matrix -- 4.2 Correlation functions -- 4.3 Thermodynamic limit -- 4.4 Connected functions and cluster properties -- 4.5 Statistical models: Simple examples -- 4.6 The Gaussian model -- 4.7 Gaussian model: The continuum limit -- 4.8 More general models: The continuum limit -- Exercises -- 5 Continuum limit and path integrals -- 5.1 Gaussian path integrals -- 5.2 Gaussian correlations. Wick's theorem -- 5.3 Perturbed Gaussian measure -- 5.4 Perturbative calculations: Examples -- Exercises -- 6 Ferromagnetic systems. Correlation functions -- 6.1 Ferromagnetic systems: Definition -- 6.2 Correlation functions. Fourier representation.
6.3 Legendre transformation and vertex functions -- 6.4 Legendre transformation and steepest descent method -- 6.5 Two- and four-point vertex functions -- Exercises -- 7 Phase transitions: Generalities and examples -- 7.1 Infinite temperature or independent spins -- 7.2 Phase transitions in infinite dimension -- 7.3 Universality in infinite space dimension -- 7.4 Transformations, fixed points and universality -- 7.5 Finite-range interactions in finite dimension -- 7.6 Ising model: Transfer matrix -- 7.7 Continuous symmetries and transfer matrix -- 7.8 Continuous symmetries and Goldstone modes -- Exercises -- 8 Quasi-Gaussian approximation: Universality, critical dimension -- 8.1 Short-range two-spin interactions -- 8.2 The Gaussian model: Two-point function -- 8.3 Gaussian model and random walk -- 8.4 Gaussian model and field integral -- 8.5 Quasi-Gaussian approximation -- 8.6 The two-point function: Universality -- 8.7 Quasi-Gaussian approximation and Landau's theory -- 8.8 Continuous symmetries and Goldstone modes -- 8.9 Corrections to the quasi-Gaussian approximation -- 8.10 Mean-field approximation and corrections -- 8.11 Tricritical points -- Exercises -- 9 Renormalization group: General formulation -- 9.1 Statistical field theory. Landau's Hamiltonian -- 9.2 Connected correlation functions. Vertex functions -- 9.3 Renormalization group: General idea -- 9.4 Hamiltonian flow: Fixed points, stability -- 9.5 The Gaussian fixed point -- 9.6 Eigen-perturbations: General analysis -- 9.7 A non-Gaussian fixed point: The & -- #949 -- -expansion -- 9.8 Eigenvalues and dimensions of local polynomials -- 10 Perturbative renormalization group: Explicit calculations -- 10.1 Critical Hamiltonian and perturbative expansion -- 10.2 Feynman diagrams at one-loop order -- 10.3 Fixed point and critical behaviour -- 10.4 Critical domain.
10.5 Models with O(N) orthogonal symmetry -- 10.6 Renormalization group near dimension 4 -- 10.7 Universal quantities: Numerical results -- 11 Renormalization group: N-component fields -- 11.1 Renormalization group: General remarks -- 11.2 Gradient flow -- 11.3 Model with cubic anisotropy -- 11.4 Explicit general expressions: RG analysis -- 11.5 Exercise: General model with two parameters -- Exercises -- 12 Statistical field theory: Perturbative expansion -- 12.1 Generating functionals -- 12.2 Gaussian field theory. Wick's theorem -- 12.3 Perturbative expansion -- 12.4 Loop expansion -- 12.5 Dimensional continuation and regularization -- Exercises -- 13 The & -- #963 -- [sup(4)] field theory near dimension 4 -- 13.1 Effective Hamiltonian. Renormalization -- 13.2 Renormalization group equations -- 13.3 Solution of RGE: The & -- #949 -- -expansion -- 13.4 Effective and renormalized interactions -- 13.5 The critical domain above T[sub(c)] -- 14 The O(N) symmetric (& -- #934 -- [sup(2)])[sup(2)] field theory in the large N limit -- 14.1 Algebraic preliminaries -- 14.2 Integration over the field & -- #934 -- : The determinant -- 14.3 The limit N & -- #8594 & -- #8734 -- : The critical domain -- 14.4 The (& -- #934 -- [sup(2)][sup(2)] field theory for N & -- #8594 & -- #8734 -- 14.5 Singular part of the free energy and equation of state -- 14.6 The (& -- #955 -- & -- #955 -- ) and (& -- #934 -- [sup(2)] & -- #934 -- [sup(2)]) two-point functions -- 14.7 Renormalization group and corrections to scaling -- 14.8 The 1/N expansion -- 14.9 The exponent η at order 1/N -- 14.10 The non-linear & -- #963 -- -model -- 15 The non-linear & -- #963 -- -model -- 15.1 The non-linear & -- #963 -- -model on the lattice -- 15.2 Low-temperature expansion -- 15.3 Formal continuum limit -- 15.4 Regularization.
15.5 Zero-momentum or IR divergences -- 15.6 Renormalization group -- 15.7 Solution of the RGE. Fixed points -- 15.8 Correlation functions: Scaling form -- 15.9 The critical domain: Critical exponents -- 15.10 Dimension 2 -- 15.11 The (& -- #934 -- [sup(2)])[sup(2)]field theory at low temperature -- 16 Functional renormalization group -- 16.1 Partial field integration and effective Hamiltonian -- 16.2 High-momentum mode integration and RGE -- 16.3 Perturbative solution: & -- #934 -- [sup(4)] theory -- 16.4 RGE: Standard form -- 16.5 Dimension 4 -- 16.6 Fixed point: & -- #949 -- -expansion -- 16.7 Local stability of the fixed point -- Appendix -- A1 Technical results -- A2 Fourier transformation: Decay and regularity -- A3 Phase transitions: General remarks -- A4 1/N expansion: Calculations -- A5 Functional renormalization group: Complements -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.
Record Nr. UNINA-9910955437603321
Zinn-Justin Jean  
Oxford, : Oxford University Press, 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui