Deceptive signals of phase transitions in small magnetic clusters.

We present an analysis of the thermodynamic properties of small transition-metal clusters and show how the commonly used indicators of phase transitions such as peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.