Scaling Theory of Quantum Critical Phenomena

Виктор Степанович Доценко

Daniel J. Amit, Víctor Martín-Mayor

Pertinent Concepts and Ideas in the Theory of Critical Phenomena Formulation of the Problem of Phase Transitions in Terms of Functional Integrals Functional Integrals in Quantum Field Theory Perturbation Theory and Feynman Graphs Vertex Functions and Symmetry Breaking Expansions in the Number of Loops and Components Renormalization The Renormalization Group and Scaling the Critical Region The Computation of the Critical Exponents Beyond Leading Scaling Universality Revisited Critical Behavior with Several Couplings Crossover Phenomena Critical Phenomena near Two Dimensions Real Space Methods Finite Size Scaling Monte Carlo Methods. Numerical Field Theory.

L. De Cesare, Dimo I. Uzunov

N. S. Tonchev

Barry M. McCoy

Abstract This chapter presents the phenomenological description of critical phenomena. It derives inequalities for critical exponents which follow from thermodynamics. It explains the scaling theory of critical phenomena of Ising-like systems, it gives scaling for Heisenberg-like systems, and introduces the concept of universality.