[...]... Point 6.3 Away from the Critical Point 6.4 Yang–Baxter Equation and R-matrix Problems 192 193 203 206 206 211 Part III 155 157 Quantum Field Theory and Conformal Invariance 7 Quantum Field Theory 7.1 Motivations 7.2 Order Parameters and Lagrangian 7.3 Field Theory of the Ising Model 7.4 Correlation Functions and Propagator 7.5 Perturbation Theory and Feynman Diagrams 7.6 Legendre Transformation and... Bernard, Andrea Cappelli, Ed Corrigan, Boris Dubrovin, Patrick Dorey, Fabian Essler, Paul Fendley, Vladimir Kravstov, Andre’ LeClair, Alexander Nersesyan, Paul Pearce, Hubert Saleur, Giuseppe Santoro, Kareljan Schoutens, Fedor Smirnov, Sasha Zamolodchikov, and Jean-Bernard Zuber I would also like to mention and thank my collaborators Carlo Acerbi, Daniel Cabra, Filippo Colomo, Alessandro De Martino, Davide... cos(π/5) = ( 5 + 1)/2 In addition to their notable properties, the exact solution provided by the integrable theories is an important step towards the general study of the scaling region close to the critical points In fact, they permit an efficient perturbative scheme to study nonintegrable effects, in particular to follow how the mass spectrum changes by varying the coupling constants Thanks to this approach,... Identity and Primary Fields 10.7 Central Charge and Virasoro Algebra 10.8 Representation Theory 10.9 Hamiltonian on a Cylinder Geometry and the Casimir Effect 10A Moebius Transformations Problems 310 310 311 315 318 320 325 329 335 344 347 354 11 Minimal Conformal Models 11.1 Introduction 11.2 Null Vectors and Kac Determinant 11.3 Unitary Representations 11.4 Minimal Models 11.5 Coulomb Gas 11.6 Landau–Ginzburg... implementations in the space of the coupling constants From this analysis, one gets to the important notion of relevant, irrelevant and marginal operators and then to the universality of the critical phenomena Chapter 9: a crucial aspect of the Ising model is its fermionic nature and this chapter is devoted to this property of the model In the continuum limit, a Dirac equation for neutral Majorana fermions... De Martino, Davide Fioravanti, Anne Koubek, Marco Moriconi, Paola Mosconi, Alessandro Mossa, Silvia Penati, Alessandro Silva, Prospero Simonetti, Galen Sotkov, Roberto Tateo, and Valentina Riva Contents Part I 1 Preliminary Notions Introduction 1.1 Phase Transitions 1.2 The Ising Model 1A Ensembles in Classical Statistical Mechanics 1B Ensembles in Quantum Statistical Mechanics Problems 2 One-dimensional... where the molecules are packed into a face-centered cubic lattice In addition to the phase transition of water, many other important phase transitions fall into this category, including Bose–Einstein condensation The second class of phase transitions consists of the continuous phase transitions, also called second-order phase transitions These have no associated latent heat and they are also characterized... statical mechanics Moreover, we will use the formulation of statistical mechanics given by the canonical ensemble The different ensembles used in statistical mechanics, both in classical and quantum physics, can be found in the appendix of this chapter Phase Transitions 7 equilibrium, namely that the spins and the surrounding environment exchange energy at a common value T of the temperature Within these... critical point This means that the phase transition taking place at Tc is the result of an extraordinary collective phenomenon that involves all the spins of the system at once This observation poses the obvious theoretical problem to understand how the short-range interactions of the spins can give rise to an effective interaction that extends to the entire system when T = Tc There is also another consideration:... second tends to maximize the entropy • Principle of energy minimization In ferromagnetic materials, the configuration of the magnetic dipoles of each atom (which we denote simply as spins) tend to minimize the total energy of the system This minimization is achieved when all spins are aligned The origin of the atomic dipole, as well as their interaction, is due to quantum effects In the following, however, . h1" alt="" Statistical Field Theory This page intentionally left blank Statistical Field Theory An Introduction to Exactly Solved Models in Statistical Physics Giuseppe Mussardo International. G. Statistical field theory : an introduction to exactly solved models in statistical physics / Giuseppe Mussardo. p. cm.—(Oxford graduate texts) ISBN 978–0–19–954758–6 (hardback) 1. Field theory. profound interdisciplinary nature and its mathematical elegance; it sets outstanding challenges in several scientific areas, such as statistical mechanics, quantum field theory, and mathematical physics. Statistical