LEADER 05575nam 2200721Ia 450 001 9910465152403321 005 20200520144314.0 010 $a0-19-966516-8 010 $a1-281-15003-7 010 $a1-4356-2187-5 010 $a0-19-152774-2 010 $a9786611150037 035 $a(CKB)2560000000298354 035 $a(EBL)415653 035 $a(OCoLC)437094019 035 $a(SSID)ssj0000220708 035 $a(PQKBManifestationID)11910788 035 $a(PQKBTitleCode)TC0000220708 035 $a(PQKBWorkID)10144739 035 $a(PQKB)11222551 035 $a(StDuBDS)EDZ0000076465 035 $a(MiAaPQ)EBC415653 035 $a(PPN)14586250X 035 $a(Au-PeEL)EBL415653 035 $a(CaPaEBR)ebr10199705 035 $a(CaONFJC)MIL115003 035 $a(EXLCZ)992560000000298354 100 $a20070131d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPhase transitions and renormalisation group$b[electronic resource] /$fJean Zinn-Justin 210 $aOxford $cOxford University Press$d2007 215 $a1 online resource (465 p.) 225 1 $aOxford graduate texts 300 $aDescription based upon print version of record. 311 $a0-19-922719-5 311 $a0-19-171110-1 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a2.3 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 327 $a4.1 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 327 $a6.2 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 327 $a7.8 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 327 $a9 Renormalization group: General formulation 330 $aThe renormalization group is one of most important theoretical concepts that has emerged in physics during the twentieth century. It explains important properties of fundamental interactions at the microscopic scale, as well as universal properties of continuous macroscopic phase transitions. - ;This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in sec 410 0$aOxford graduate texts. 606 $aPhase transformations (Statistical physics) 606 $aRenormalization (Physics) 608 $aElectronic books. 615 0$aPhase transformations (Statistical physics) 615 0$aRenormalization (Physics) 676 $a530.414 700 $aZinn-Justin$b Jean$044579 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465152403321 996 $aPhase transitions and renormalisation group$92106352 997 $aUNINA