# Correlation lengths in quasi-one-dimensional systems via transfer matrices

@article{Hu2018CorrelationLI,
title={Correlation lengths in quasi-one-dimensional systems via transfer matrices},
author={Yi Hu and Lin Fu and Patrick Charbonneau},
journal={Molecular Physics},
year={2018},
volume={116},
pages={3345 - 3354}
}
• Published 2 April 2018
• Physics
• Molecular Physics
ABSTRACT Using transfer matrices up to next-nearest-neighbour interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers [Fu et al., Soft Matter 13, 3296 (2017)]. Here, we identify the theoretical basis for these behaviours. In particular, we…
10 Citations
Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system
• Physics, Materials Science
• 2020
Molecular dynamics computer simulations of collective excitations in a system of hard disks confined to a narrow channel of the specific width, that resembles 2D triangular lattice at disk close
Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices
• Physics
Physical Review B
• 2021
Ising models with frustrated next-nearest-neighbor interactions present a rich morphology of modulated phases. These phases, however, assemble and relax slowly, which hinders their computational
Highly confined mixtures of parallel hard squares: A density-functional-theory study.
• Physics, Medicine
Physical review. E
• 2019
It is claimed that, although exact calculations exclude the existence of true phase transitions in (1+ε)-dimensional systems, density-functional theory is still successful in describing packing properties of large clusters of particles.
Comment on “Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system”
• Physics
Physical Review Research
• 2021
Huerta et al. [Phys. Rev. Research 2, 033351 (2020)] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a
Resolving the two-dimensional ANNNI model using transfer matrices
• Physics
• 2020
The phase diagram of the two-dimensional ANNNI model has long been theoretically debated. Extremely long structural correlations and relaxation times further result in numerical simulations making
Inherent structure landscape of hard spheres confined to narrow cylindrical channels
• Physics
Physical Review E
• 2021
Mahdi Zarif, ∗ Raymond J. Spiteri, and Richard K. Bowles 4, † Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran. Department of Computer Science,
Analytical canonical partition function of a quasi-one-dimensional system of hard disks.
The exact canonical partition function of a hard disk system in a narrow quasi-one-dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result, the many
Marginally jammed states of hard disks in a one-dimensional channel.
• Physics, Medicine
Physical review. E
• 2020
This work shows that there exist jammed states not found within the tiling approach of Ashwin and Bowles, and the most dense of these marginal states is an unusual state of matter that is asymptotically crystalline.
The Gardner correlation length scale in glasses
• Physics, Materials Science
• 2020
The Gardner length scale $\xi$ is the correlation length in the vicinity of the Gardner transition, which is an avoided transition in glasses where the phase space of the glassy phase fractures into

## References

SHOWING 1-10 OF 90 REFERENCES
Critical behavior of hard squares in strong confinement.
• Mathematics, Physics
Physical review. E
• 2017
The phase behavior of a quasi-one-dimensional system of hard squares with side-length σ, where the particles are confined between two parallel walls and only nearest-neighbor interactions occur is examined, and it is found that this structural change becomes critical at the (p_{c},H_{c}) point.
Hard particles in narrow pores. Transfer-matrix solution and the periodic narrow box
• Chemistry
• 1993
We derive an exact transfer‐matrix solution for an infinite system of hard particles confined in a manner that precludes non‐nearest‐neighbor interactions. The solution takes the form of a functional
Structural properties of hard disks in a narrow tube
• Physics
• 2011
Positional ordering of a two-dimensional fluid of hard disks is examined in tubes so narrow that only nearest neighbor interactions take place. Using the exact transfer-matrix method the transverse
Inherent structures, fragility, and jamming: insights from quasi-one-dimensional hard disks.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
A quasi-one-dimensional system of hard disks confined between hard lines is studied to explore the relationship between the inherent structure landscape, the thermodynamics, and the dynamics of the fluid and shows that the system exhibits a crossover from fragile to strong fluid behavior.
Glasslike behavior of a hard-disk fluid confined to a narrow channel.
• Physics, Medicine
Physical review. E
• 2016
The caging behavior of the disks that sets in at characteristic packing fraction ϕ(d) is studied and four-point overlap functions similar to those studied when investigating dynamical heterogeneities are determined and the time-dependent dynamical length scale has been extracted.
Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares.
• Physics, Medicine
The Journal of chemical physics
• 2015
An eigenvalue equation is derived for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square).
Static and dynamical properties of a hard-disk fluid confined to a narrow channel.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
The thermodynamic properties of disks moving in a channel sufficiently narrow that they can collide only with their nearest neighbors can be solved exactly by determining the eigenvalues and eigenfunctions of an integral equation, and an approximate solution is developed which becomes exact in the high-density limit.
Understanding the ideal glass transition: lessons from an equilibrium study of hard disks in a channel.
• Physics, Medicine
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2015
It is argued that the α-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ϕ(K), which is larger than the penetration lengths that have been reported for three-dimensional systems.
Fragile-strong fluid crossover and universal relaxation times in a confined hard-disk fluid.
• Physics, Medicine
Physical review letters
• 2012
Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adam-Gibbs relation does not predict the relaxation behavior.
Clustering and assembly dynamics of a one-dimensional microphase former.
• Physics, Medicine
Soft matter
• 2018
This work studies the disordered regime of a one-dimensional SALR model, whose simplicity enables detailed analysis by transfer matrices and Monte Carlo simulations, and finds that cluster moves markedly accelerate the mixing time, but that event chains are of limited help in the clustering regime.