Anomalous Binder Cumulant and Lack of Self-Averageness in Systems with Quenched Disorder

Details Anomalous Binder Cumulant and Lack of Self-Averageness in Systems with Quenched Disorder Anomalous Binder Cumulant and Lack of Self-Averageness in Systems with Quenched Disorder

2006-11-20

arxiv.org/abs/cond-mat/0611509v1

J. Korean Phys. Soc. 49, L1885 (2006)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample fluctuations. We study the globally coupled Kuramoto model of interacting limit-cycle oscillators with random natural frequencies and find an anomalous dip in the BC near the transition. We show that the dip is related to non-self-averageness of the order parameter at the transition. Alternative definitions of the BC, which do not show any anomalous behavior regardless of the existence of non-self-averageness, are proposed.

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