Boundary between long-range and short-range critical behavior in systems with algebraic interactions.
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.
Luijten
Erik
E
Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA. luijten@uiuc.edu
Blöte
Henk W J
HW
D000465:Algorithms; D008962:Models, Theoretical; D009010:Monte Carlo Method