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

Preprint

28 December 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/0112472

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.

Keywords

RANGE CRITICAL BEHAVIOR
PHASE TRANSITIONS
MONTE CARLO
POWER LAW
DECAY
ISING

All Related Versions

Version 1, 2001-12-28, ArXiv
Published version: Physical Review Letters, 89 (2), 025703.

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