title: Boundary between long-range and short-range critical behavior in systems with algebraic interactions.
abstract: We investigate phase transitions of two-dimensional Ising models with power-law interactions, using an efficient Monte Carlo algorithm. For slow decay, the transition is of the mean-field type; for fast decay, it belongs to the short-range Ising universality class. We focus on the intermediate range, where the critical exponents depend continuously on the power law. We find that the boundary with short-range critical behavior occurs for interactions depending on distance r as r(-15/4). This answers a long-standing controversy between mutually conflicting renormalization-group analyses.
authors.affiliation: Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA. luijten@uiuc.edu
authors.forename: Erik
authors.initials: E
authors.lastname: Luijten
authors.forename: Henk W J
authors.initials: HW
authors.lastname: Blöte
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D009010:Monte Carlo Method