The boundary between long-range and short-range critical behavior
Statistical Mechanics
2009-11-07 v1
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.
Cite
@article{arxiv.cond-mat/0112472,
title = {The boundary between long-range and short-range critical behavior},
author = {Erik Luijten and Henk W. J. Blöte},
journal= {arXiv preprint arXiv:cond-mat/0112472},
year = {2009}
}
Comments
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