Pseudo-Critical Phenomena in the Fisher-Domb Cluster Model: Cluster Picture for Pseudospinodals in First-Order Transitions

Cluster dynamics for first-order phase transitions in the Potts model.

Surface Critical Phenomena at First-order Phase Transitions

Frequently, first-order phase transitions in solids are characterized by the coexistence of a disordered phase and several ordered phases. Near such a transition, the disordered phase may appear in the surface region of the crystal even though the bulk crystal remains in one of its ordered states. This leads to several critical effects which are characterized by critical exponents. Recent exper...

Critical Phenomena with Linked Cluster Expansions in a Finite Volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish 1st from 2nd order transitions within a finite size scaling analysis. The criterion applies also to other methods for investigating the phase structure such ...

Cluster aggregation model for discontinuous percolation transitions.

The evolution of the Erdos-Rényi (ER) network by adding edges is a basis model for irreversible kinetic aggregation phenomena. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel Kij approximately ij , where ij is the product of the sizes of two merging clusters. Here we study that when the giant cluster is discoura...

Tracing cluster transitions for different cluster types

Clustering algorithms detect groups of similar population members, like customers, news or genes. In many clustering applications the observed population evolves and changes, subject to internal and external factors. Detecting and understanding change is important for decision support. We extend our earlier framework MONIC for cluster transition modeling and detection, into MONIC for cluster-ty...