Finite temperature crossover from a crystalline to a cluster phase for a confined finite chain of ions

TL;DR

This study uses Monte Carlo simulations to explore how a one-dimensional chain of equally charged particles transitions from a crystalline to a cluster phase as temperature increases, revealing non-extensive behavior and distinct statistical properties.

Contribution

It provides the first detailed analysis of the temperature-induced crossover in a confined one-dimensional ion chain, highlighting the role of long-range interactions and trap parameters.

Findings

Transition temperature depends on particle number and box size

Spacing distribution shifts from discrete peaks to Gaussian and exponential forms

Heat capacity exhibits a clear signature of the crossover

Abstract

Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles N and the box size L, implying non-extensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form whereas in the high temperature regime an exponential decay is observed. The high temperature behaviour shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the non-linear behaviour of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.