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DY: Fachverband Dynamik und Statistische Physik
DY 22: Poster: Statistical Physics
DY 22.27: Poster
Wednesday, March 19, 2025, 10:00–12:00, P3
Criticality and Percolation in the Off-Lattice XY Model — •Manthan Chattopadhyay, Thomas Richard Ullmann, and Klaus Kroy — Institute for Theoretical Physics, Leipzig University, 04103 Leipzig, Germany
We investigate the critical behavior of the 2D XY model with quenched positional disorder by distributing spins randomly via a spatial Poisson point process. This off-lattice approach allows us to study how quenched disorder affects phase transitions and critical phenomena, with the primary focus being the critical power-law scaling between the Kosterlitz-Thouless transition temperature Tc and the mean spin density ⟨ ρ ⟩. Using both a homogeneous coarse-graining method and percolation theory, we derive predictions for the scaling Tc ∝ (⟨ ρ ⟩ − ⟨ ρc ⟩ )ζ. By considering the fractal nature of the spin network near the percolation threshold, characterized by the fractal dimension Df, the exponent is estimated. Simulation results confirm the existence of a percolation threshold with an exponent obtained from simulations similar to those of our analytic work, aligning closely with theoretical prediction. The fractal nature of the spin network near ⟨ ρc ⟩ is validated through the box-counting method, which is consistent with the value for 2D percolation. At high densities well above the percolation threshold, critical exponents approach expected values of the XY universality class, and the magnetization exponent β conforms to empirical observations in ultrathin magnetic films.
Keywords: percolation; spin; off-lattice; graph; scaling