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The boundary between long-range and short-range critical behavior

Erik Luijten·Henk W. J. Blöte
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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.

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Erik Luijten, Henk W. J. Blöte. 2001-12-27. The boundary between long-range and short-range critical behavior. https://doi.org/10.1103/physrevlett.89.025703

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