Melting of the two-dimensional solid phase in the Gaussian-core model

Abstract

A general theory for the melting of two dimensional solids explaining the universal and non-universal properties is an open problem up to date. Although the celebrated KTHNY theory have been able to predict the critical properties of the melting transition in a variety cases, it is already known that it is not able to capture the occurrence of first order transitions observed in certain systems as well as it doesn't provide a clear way to calculate the melting temperature for a specific model. In the present work we have developed an analytical method that combines Self Consistent Variational Approximation with the Renormalization Group in order to deal simultaneously with the phonon fluctuations and the topological defects present in the melting process of two dimensional crystals. The method was applied with impressive success to the study of the phase diagram of the Gaussian-core model, capturing not only the reentrant feature of its 2D solid phase, but also the related critical temperatures as a function of the density in quantitative detail. The developed method can be directly applied to study the melting of any hexagonal simple crystal formed by particles interacting through any finite pairwise interaction potential. Additionally, it has the potential to explain the occurrence of first order transitions in the melting process of two dimensional crystals.

References in corpus (12)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Soft Spheres Make More Mesophases
• Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex-core energy
• Attraction tames two-dimensional melting: from continuous to discontinuous transitions
• Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions
• $BKT$ transitions in classical and quantum long-range systems
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Density functional theory of freezing for soft interactions in two dimensions
• On the accuracy of the melting curves drawn from modelling a solid as an elastic medium
• Coarse grained models of stripe forming systems: phase diagrams, anomalies and scaling hypothesis
• Self-consistent harmonic approximation with non-local couplings

Cited by in corpus (2)

• Short-wavelength mesophases in the ground states of core-softened particles in two-dimensions
• Topological transition and emergent elasticity of dislocation in skyrmion lattice: Beyond Kittel's magnetic-polar analogy