ABSTRACT

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental theoretical concepts such as mean field theory, the scaling hypothesis, and the renormalization group. He then goes on to apply the renormalization group to selected problems, with emphasis on the underlying physics and the basic assumptions involved.

chapter |4 pages

SUMMARY

chapter 2|5 pages

QUALITATIVE PICTURE

chapter 3|6 pages

THERMODYNAMIC PROPERTIES AND EXPONENTS

chapter 7|6 pages

MEAN FIELD THEORY

chapter |5 pages

SUMMARY

chapter 2|5 pages

CLASSICAL MODELS OF THE CELL HAMILTONIAN

chapter 3|6 pages

STATISTICAL MECHANICS

chapter 5|5 pages

GINZBURG-LANDAU FORM

chapter |1 pages

SUMMARY

chapter 3|4 pages

GAUSSIAN APPROXIMATION FOR T > Tc

chapter 4|3 pages

GAUSSIAN APPROXIMATION FOR T < Tc

chapter 7|4 pages

FLUCTUATION AND DIMENSION

chapter 8|3 pages

DISCUSSION

chapter |5 pages

SUMMARY

chapter 3|2 pages

DISCUSSION

chapter |3 pages

SUMMARY

chapter 3|4 pages

ALTERNATIVES IN DEFINING THE RG

chapter 4|1 pages

CONCLUDING REMARK

chapter |1 pages

SUMMARY

chapter 1|4 pages

THE FIXED POINT AND ITS NEIGHBORHOOD

chapter 3|8 pages

THE FREE ENERGY

chapter 4|2 pages

CRITICAL REGION

chapter 5|4 pages

SUMMARY AND REMARKS

chapter |1 pages

SUMMARY

chapter 1|5 pages

THE GAUSSIAN FIXED POINT

chapter 4|3 pages

CRITICAL EXPONENTS FOR d > 4

chapter 6|12 pages

EFFECT OF OTHER O(ε2) TERMS IN Rsμ

chapter |1 pages

SUMMARY

chapter 1|9 pages

THE RG IN THE LARGE-n LIMIT

chapter 2|11 pages

WILSON'S RECURSION FORMULA

chapter 3|4 pages

APPLICATION TO THE n → ∞

chapter 4|16 pages

DEFINITIONS OF THE RG FOR DISCRETE SPINS

chapter 6|6 pages

DISCUSSION

chapter |1 pages

SUMMARY

chapter 4|8 pages

THE 1/n EXPANSION OF CRITICAL EXPONENTS

chapter 5|5 pages

THE ε EXPANSION OF CRITICAL EXPONENTS

chapter 8|3 pages

REMARKS

chapter 9|7 pages

THE RG IN THE PERTURBATION EXPANSION

chapter |11 pages

SUMMARY

chapter 2|12 pages

THE RG APPROACH TO NONMAGNETIC IMPURITIES

chapter 4|10 pages

COMMENTS ON GRAPHS

chapter 5|14 pages

THE SELF-AVOIDING RANDOM WALK PROBLEM

chapter 6|6 pages

OTHER NON-IDEAL FEATURES OF REAL SYSTEMS

chapter |5 pages

SUMMARY

chapter 2|7 pages

BROWNIAN MOTION AND KINETIC EQUATIONS

chapter 3|3 pages

RELAXATION TIMES

chapter 4|4 pages

ELIMINATION OF FAST MODES

chapter 6|8 pages

THE VAN HOVE THEORY

chapter |4 pages

SUMMARY

chapter |1 pages

SUMMARY

chapter 2|16 pages

EFFECTS OF SLOW HEAT CONDUCTION

chapter 3|6 pages

THE ISOTROPIC FERROMAGNET

chapter 4|4 pages

UNIVERSALITY IN CRITICAL DYNAMICS

chapter |3 pages

SUMMARY

chapter 3|6 pages

THE FLUCTUATION-DISSIPATION THEOREM

chapter 2|7 pages

SMOOTH CUTOFF