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First and second order clustering transitions for a system with infinite-range attractive interaction

Mickael Antoni·Stefano Ruffo·Alessandro Torcini
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Abstract

We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in a unique cluster. At higher energy it exhibits a transition towards a homogenous phase. For sufficiently strong coupling $A$ an intermediate phase characterized by two clusters appears. Depending on the value of $A$ the observed transitions can be either second or first order in the canonical ensemble. In the latter case microcanonical results differ dramatically from canonical ones. However, a canonical analysis, extended to metastable and unstable states, is able to describe the microcanonical equilibrium phase. In particular, a microcanonical negative specific heat regime is observed in the proximity of the transition whenever it is canonically discontinuous. In this regime, {\it microcanonically stable} states are shown to correspond to {\it saddles} of the Helmholtz free energy, located inside the spinodal region.

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Mickael Antoni, Stefano Ruffo, Alessandro Torcini. 2002-06-19. First and second order clustering transitions for a system with infinite-range attractive interaction. https://doi.org/10.1103/physreve.66.025103

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