Branched Polymers with Loops

Abstract

We propose a classification of critical behaviours of branched polymers for arbitrary topology. We show that in an appropriately defined double scaling limit the singular part of the partition function is universal. We calculate this partition function exactly in the generic case and perturbatively otherwise. In the discussion section we comment on the relation between branched polymer theory and Euclidean quantum gravity.

11 pages LaTeX

References in corpus (4)

• Focusing on the Fixed Point of 4D Simplicial Gravity
• Multi-spin systems on a randomly triangulated surface
• Long range correlations in branched polymers
• From Weak to Strong Coupling in Two-Dimensional Gravity

Cited by in corpus (19)

• Reconstructing the Universe
• Statistical ensemble of scale-free random graphs
• Tree Networks with Causal Structure
• Finite size scaling of the balls in boxes model
• 4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields
• 4d Simplicial Quantum Gravity: Matter Fields and the Corresponding Effective Action
• Summing over all Topologies in CDT String Field Theory
• Charged solitons in branched conducting polymers
• Exciton dynamics in branched conducting polymers: Quantum graphs based approach
• Collapse of 4D random geometries
• Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity
• Exotic trees
• Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity
• Matter Correlations in Branched Polymers
• Random manifolds and quantum gravity
• Balls in Boxes and Quantum Gravity
• Correlation functions and critical behaviour on fluctuating geometries
• Long-range disassortative correlations in generic random trees
• Branched polymers with loops coupled to the critical Ising model