Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

Perturbative Topological Field Theory

We give a review of the application of perturbative techniques to topologi-cal quantum eld theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.

Topological transitions in Berry's phase interference effects.

More is the Same; Phase Transitions and Mean Field Theories

This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of “singularity”, “order parameter”, “mean field theory”, “variational method”, “correlation len...

Tricritical Wedge Filling Transitions with Short-ranged Forces

We show that the 3D wedge filling transition in the presence of shortranged interactions can be first-order or second order depending on the strength of the line tension associated with to the wedge bottom. This fact implies the existence of a tricritical point characterized by a short-distance expansion which differs from the usual continuous filling transition. Our analysis is based on an eff...

Rigorous Analysis of Discontinuous Phase Transitions via Mean-field Bounds

We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition t...