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Boundary between long-range and short-range critical behavior in systems with algebraic interactions



Boundary between long-range and short-range critical behavior in systems with algebraic interactions



Physical Review Letters 89(2): 025703



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.

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Accession: 045396683

Download citation: RISBibTeXText

PMID: 12097006

DOI: 10.1103/physrevlett.89.025703


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