LEADER 04918nam 2200661Ia 450 001 9910458637003321 005 20200520144314.0 010 $a1-281-91859-8 010 $a9786611918590 010 $a981-270-876-6 035 $a(CKB)1000000000402253 035 $a(EBL)1193071 035 $a(SSID)ssj0000305216 035 $a(PQKBManifestationID)11245023 035 $a(PQKBTitleCode)TC0000305216 035 $a(PQKBWorkID)10285906 035 $a(PQKB)10602967 035 $a(MiAaPQ)EBC1193071 035 $a(WSP)00006482 035 $a(Au-PeEL)EBL1193071 035 $a(CaPaEBR)ebr10698794 035 $a(CaONFJC)MIL191859 035 $a(OCoLC)747539595 035 $a(EXLCZ)991000000000402253 100 $a20070828d2007 uy 0 101 0 $aeng 135 $aurcnu---unuuu 181 $ctxt 182 $cc 183 $acr 200 00$aOrder, disorder and criticality$b[electronic resource] $hVolume 2 $eadvanced problems of phase transition theory /$feditor, Yurij Holovatch 210 $aHackensack, NJ ;$aLondon $cWorld Scientific$d2007 215 $a1 online resource (308 p.) 225 1 $aAdvanced Problems of Phase Transition Theory ;$vv.2 300 $aDescription based upon print version of record. 311 $a981-270-767-0 320 $aIncludes bibliographical references and index. 327 $aCONTENTS; Preface; Introduction to the Non-Perturbative Renormalization Group Bertrand Delamotte; Contents; 1. Wilson's Renormalization Group; 1.1. Introduction; 1.2. The Perturbative Method in Field Theory; 1.3. Wilson's Approach to the Renormalization Group; 2. Renormalization Group Transformations; 2.1. Blocks of Spins; 2.2. Two Remarks Concerning RG Transformations; 2.3. Linear RG Transformations and Correlation Length; 3. Properties of the RG Flow: Fixed Points, Critical Surface, Relevant Directions; 3.1. Scaling Relations - Linearization of the Flow Around the Fixed Point 327 $a3.2. The Correlation Length and the Spin-Spin Correlation Function 3.3. Scaling of the Correlation Function in the Presence of a Magnetic Field - Relation Among Exponents; 3.4. The Example of the Two-Dimensional Ising Model on the Triangular Lattice; 4. The Non-Perturbative Renormalization Group; 4.1. Introduction; 4.1.1. The Wilson-Polchinski Approach; 4.2. The Effective Average Action Method; 4.2.1. Block-Spins, Coarse Graining, Legendre Transform, etc.; 4.3. An Integral Representation of ?k and the Limit k; 5. The Exact RG Equation and Its Properties 327 $a9.2. The RG Equation for the Dimensionless Potential ?U k9.3. The Limits d 4, d 2 and N; 10. Conclusion; Acknowledgements; Appendix A. Definitions, conventions; Appendix B. The Exact RG equations; Appendix B.1. RG equation for Wk[B]; Appendix B.2. RG equation for ?k[M]; Appendix B.3. RG equation for the elective potential; References; Introduction to Critical Dynamics Reinhard Folk; Contents; 1. Introduction; 2. Experimental Evidence; 2.1. Fluids; 2.2. Light Scattering; 2.3. Ferromagnets; 2.4. Super fluid 4He; 3. Van Hove Theory; 4. Dynamical Scaling 327 $a4.1. Scaling Form of the Dynamic Susceptibility 4.2. Finding the Dynamical Exponent z by Scaling Relations; 4.2.1. Ferromagnet; 4.2.2. Fluids; 4.2.3. Superfluid Transition; 5. From Dynamic Equations to a Lagrangian; 5.1. Static Functional; 5.2. Dynamic Equations; 5.3. Dynamic Functional; 5.4. Renormalization; 6. Renormalization and the Dynamical Exponent; 6.1. Structure and Renormalization; 6.2. Calculating the Dynamical Exponent; 6.2.1. Models without Mode Coupling Terms; 6.2.2. Models with Mode Coupling Terms; 7. Comparison with Experiment; 7.1. General Procedure 327 $a7.2. Fluids: The Linewidth in Light Scattering 330 $aThis book is the second volume of review papers on advanced problems of phase transitions and critical phenomena, following the success of the first volume in 2004. Broadly, the volume aims to demonstrate that the phase transition theory, which experienced its 'golden age' during the 70's and 80's, is far from over and there is still a good deal of work to be done, both at the fundamental level and in respect of applications.The topics presented in this volume include: critical behavior as explained by the non-perturbative renormalization group, critical dynamics, a spacetime approach to phase t 410 0$aAdvanced Problems of Phase Transition Theory 606 $aPhase transformations (Statistical physics) 606 $aStatistical physics 608 $aElectronic books. 615 0$aPhase transformations (Statistical physics) 615 0$aStatistical physics. 676 $a530.4/74 701 $aHolovatch$b Yurij$0861687 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458637003321 996 $aOrder, disorder and criticality$91922805 997 $aUNINA