1999/10/01 by H. -O. Georgii, Hans-Otto Georgii, Georgii, H. -O.
Mathematics · Physics and Astronomy · #60G55 #60K35 #82B05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G55 #msc:60K35 #msc:82B05
paper · pdf · doi:10.48550/arxiv.math/9910005
Survey article, 25 pages
arxiv created 1999/10/01 · openalex publication_date 1999/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction process and on perfect simulation.