Multicritical Crossover Scaling Functions.
Abstract
The critical behavior of a system is investigated, for example an antiferromagnet, which displays a multicritical point of bicritical or tetracritical character. Crossover sealing functions for the most important thermodynamic functions are calculated, to first order in e = 4 - d, where d is the dimensionality of space, and displayed graphically. The mechanism by which an irrelevant cubic perturbation induces tetracritical behavior is investigated and clarified. The differential recursion relations are solved to O(e), up to a point where one or more components of the order parameter are no longer critical. Those components are then integrated out, yielding a reduced Hamiltonian for the remaining components. The procedure is then repeated; the new recursion relations being again integrated until the remaining components become noncritical. The results are thus matched onto a noncritical system that can be treated perturbatively.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- November 1977
- Bibcode:
- 1977PhDT........22D
- Keywords:
-
- Physics: Condensed Matter;
- Critical Point;
- Crossovers;
- Scaling Laws;
- Computation;
- Hamiltonian Functions;
- Recursive Functions;
- Thermodynamics;
- Solid-State Physics