An on-lattice model for two-dimensional melting
Abstract
We introduce an on-lattice minimal model of two-dimensional melting, a clock model with vacancies with control parameters temperature, chemical potential and external field. We study the full phase diagram using cluster Monte Carlo, Tensor Network Renormalisation Group and selfconsistent mean field methods. A non-universal ensemble of melting scenarios is observed including the KTHNY scenario of two Berezinskii-Kosterlitz-Thouless phase transitions delimiting a quasilong-range ordered phase. The upper transition evolves into first-order transition in analogy with simulations on hard and soft discs and at low chemical potential there is a single transition between ordered high density and disordered low density phases. The evolution is via a special tricritical point that is accessed in detail. This work therefore provides a framework for understanding the crossover between 2D melting scenarios and offers insights into the behavior of realistic systems.
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BibTeX
@misc{roge2026onlattice,
title = {{An on-lattice model for two-dimensional melting}},
author = {Antonin Rogé and Peter Holdsworth and Alexis Poncet},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13110},
eprint = {2609.13110},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05780603v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - An on-lattice model for two-dimensional melting
AU - Antonin Rogé
AU - Peter Holdsworth
AU - Alexis Poncet
PY - 2026
DA - 2026/09/11
PB - HAL
DO - 10.48550/arxiv.2609.13110
UR - https://hal.science/hal-05780603v1
AB - We introduce an on-lattice minimal model of two-dimensional melting, a clock model with vacancies with control parameters temperature, chemical potential and external field. We study the full phase diagram using cluster Monte Carlo, Tensor Network Renormalisation Group and selfconsistent mean field methods. A non-universal ensemble of melting scenarios is observed including the KTHNY scenario of two Berezinskii-Kosterlitz-Thouless phase transitions delimiting a quasilong-range ordered phase. The upper transition evolves into first-order transition in analogy with simulations on hard and soft discs and at low chemical potential there is a single transition between ordered high density and disordered low density phases. The evolution is via a special tricritical point that is accessed in detail. This work therefore provides a framework for understanding the crossover between 2D melting scenarios and offers insights into the behavior of realistic systems.
ER -