Metastability, negative specific heat and weak mixing in classical long-range many-rotator system

Abstract

We perform a molecular dynamical study of the isolated $d=1$ classical Hamiltonian ${\cal H} = {1/2} \sum_{i=1}^N L_i^2 + \sum_{i \ne j} \frac{1-cos(θ_i-θ_j)}{r_{ij}^α} ;(α\ge 0)$, known to exhibit a second order phase transition, being disordered for $u \equiv U/N{\tilde N} \ge u_c(α,d)$ and ordered otherwise ($U\equiv$ total energy and ${\tilde N} \equiv \frac{N^{1-α/d}-α/d}{1-α/d}$). We focus on the nonextensive case $α/d \le 1$ and observe that, for $u u_c$, hence decreases from 1/9 to zero when $α/d$ increases from zero to unity, remaining zero thereafter. This new and simple {\it connection between anomalies above and below the critical point} reinforces the nonextensive universality scenario.