Unsupervised identification of topological phase transitions using predictive models

Topological Aspects of Phase Transitions

In the past decade and a half, an alternative analysis of phase transitions, based in the topological behavior of system configuration spaces, has been introduced. This method offers a new understanding of many phase transitions, particularly those in finite systems, using topology and manifold behavior. While the broadest hypotheses offered by researchers have proven overly optimistic, the met...

Identification of age-structured models: cell cycle phase transitions.

A methodology is developed that determines age-specific transition rates between cell cycle phases during balanced growth by utilizing age-structured population balance equations. Age-distributed models are the simplest way to account for varied behavior of individual cells. However, this simplicity is offset by difficulties in making observations of age distributions, so age-distributed models...

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P 5aN points that are uniformly distributed in all the directions but one on the N-dimensional space. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two Gaussians of variable separation and width. The typical optimal performance is measured ...

Topological Phase Transitions in Multicomponent Superconductors.

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric sy...

Topological transitions in Berry's phase interference effects.