A combinatorial proof of Rayleigh monotonicity for graphs

Cibulka, J.; Hladky, J.; LaCroix, M. A.; Wagner, D. G.

doi:10.48550/arxiv.0804.0027

Search citation statements

Order By: Relevance

Paper Sections

Select...

The Symmetry Breaking1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2009

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is proven by Feder and Mihail [40] in the wider context of balanced matroids (and uniform weights). See also [41] for a purely combinatorial proof of the stronger Raileigh condition, in the weighted case. The random cluster model for q > 1 is known to be positive associated.…”

Section: The Symmetry Breakingmentioning

confidence: 99%

Phase transition in the spanning-hyperforest model on complete hypergraphs

2009

View full text Add to dashboard Cite

By using our novel Grassmann formulation we study the phase transition of the spanning-hyperforest model of the k-uniform complete hypergraph for any k ≥ 2. The case k = 2 reduces to the spanning-forest model on the complete graph. Different k are studied at once by using a microcanonical ensemble in which the number of hyperforests is fixed. The low-temperature phase is characterized by the appearance of a giant hyperforest. The phase transition occurs when the number of hyperforests is a fraction (k − 1)/k of the total number of vertices. The behaviour at criticality is also studied by means of the coalescence of two saddle points. As the Grassmann formulation exhibits a global supersymmetry we show that the phase transition is second order and is associated to supersymmetry breaking and we explore the pure thermodynamical phase at low temperature by introducing an explicit breaking field.

show abstract

Section: The Symmetry Breakingmentioning

confidence: 99%