Kirkham, Jennifer E (1980) O3 field theory and critical phenomena. University of Southampton, Doctoral Thesis.
Abstract
In this thesis we investigate the critical behaviour for systems whose symmetry permits trilinear (03) interactions in the field $. Perturbative calculations using the renormalisation group formalism permit the critical exponents to be obtained as a power series in e - 6 - d, where d is the dimension of space. We begin with an 0(e2) calculation using the symmetry point renormalisation scheme and then discuss the extension of this scheme to 0(e3). We also discuss the possible use of a minimal subtraction renormalisation scheme in which we include the counter terms explicitly.A specific example of a 03 field theory, the Yang-Lee edge singularity, is also considered. We review the use of the instanton formalism which shows that this field theory is well defined, with a stable ground state and an oscillatory perturbation series. We further show that the contributions from the 04 terms which also arise for this singularity, are likely to be insignificant compared with those from the 03 interaction, as the dimension of space is lowered through.
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