Statistical mechanics of classical fractons on a line
Abstract
We study the equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and symmetry by forming non-equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-Laplacian and matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg--Mermin--Wagner--Coleman argument, supported by finite-size scaling, implies symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC) algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in Hamiltonian dynamics. The equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the liquid.
Related
BibTeX
@misc{sadki2026statistical,
title = {{Statistical mechanics of classical fractons on a line}},
author = {Ylias Sadki and Abhishodh Prakash and S. L. Sondhi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25999},
eprint = {2609.25999},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25999},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Statistical mechanics of classical fractons on a line
AU - Ylias Sadki
AU - Abhishodh Prakash
AU - S. L. Sondhi
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25999
UR - https://arxiv.org/abs/2609.25999
AB - We study the equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and symmetry by forming non-equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-Laplacian and matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg--Mermin--Wagner--Coleman argument, supported by finite-size scaling, implies symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC) algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in Hamiltonian dynamics. The equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the liquid.
ER -