Randomly Branched Polymers

Statistical Mechanics of Randomly Branched Polymers

The scaling behavior and conformational transitions of branched clusters are investigated using advanced Monte Carlo simulations, exact enumeration, and field-theoretic approaches to establish a universal framework. By generalizing the pruned-enriched Rosenbluth method (PERM) from linear chains to branched structures, this work deploys a recursive sampling strategy with population control. This highly efficient approach overcomes the exponential growth of configuration spaces, enabling precise scaling assessments of both animals and trees from low-dimensional spaces up to the upper critical dimension.

Universal Scaling and Logarithmic Corrections: Systematic evaluation of universal scaling exponents, partition sums, and conformational properties of branched structures across various dimensions. Using PERM to simulate configurations with controlled bias, this work tests the Parisi-Sourlas connection and determines logarithmic corrections to scaling for animals and trees at the upper critical dimension (d = 8).

"Scaling Behaviour of Lattice Animals at the Upper Critical Dimension", Euro. Phys. J. B 83, 245 (2011).

"Simulations of lattice animals and trees", J. Phys. A: Math. Gen. 38, 775 (2005).

Geometrical Constraints and Conformal Invariance: Investigation into how spatial boundaries and complex structural anchor points alter universal critical behavior. This research examines clusters grafted to low-dimensional geometric constraints, capturing exact scaling deviations and the breakdown of conformal invariance when configurations are bound to structural interfaces like wedges, cones, and branch points of Riemann surfaces.

"Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces", Phys. Rev. E 71, 065104R (2005).