# Melting of a two-dimensional monodisperse cluster crystal to a cluster liquid

## TL;DR

This study investigates the melting transition of a two-dimensional monodisperse cluster crystal into a cluster liquid, revealing a first-order phase change through simulations and mean-field analysis.

## Contribution

It provides a mean-field description of the cluster-crystal ground state and compares Monte Carlo algorithms for sampling challenges.

## Key findings

- The phase transition is of first order.
- The liquid phase is identified as a cluster liquid.
- Monte Carlo methods' efficiency varies across algorithms.

## Abstract

Monodisperse ensembles of particles that have cluster crystalline phases at low temperatures can model a number of physical systems, such as vortices in type-1.5 superconductors, colloidal suspensions and cold atoms. In this work we study a two-dimensional cluster-forming particle system interacting via an ultrasoft potential. We present a simple mean-field characterization of the cluster-crystal ground state, corroborating with Monte Carlo simulations for a wide range of densities. The efficiency of several Monte Carlo algorithms are compared and the challenges of thermal equilibrium sampling are identified. We demonstrate that the liquid to cluster-crystal phase transition is of first order and occurs in a single step, and the liquid phase is a cluster liquid.