Phys. Rev. Lett. 89, 025703 (2002) [4 pages]Boundary between Long-Range and Short-Range Critical Behavior in Systems with Algebraic InteractionsReceived 27 December 2001; published 20 June 2002 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. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.89.025703
DOI:
10.1103/PhysRevLett.89.025703
PACS:
64.60.Ak, 05.70.Jk, 64.60.Fr, 75.10.Hk
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