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Title: Avoided criticality and slow relaxation in frustrated two-dimensional models

Abstract

Here, frustration and the associated phenomenon of “avoided criticality” have been proposed as an explanation for the dramatic relaxation slowdown in glass-forming liquids. To test this, we have undertaken a Monte Carlo study of possibly the simplest such problem, the two-dimensional XY model with frustration corresponding to a small flux f per plaquette. At f = 0, there is a Berezinskii-Kosterlitz-Thouless transition at T*, but at any small but nonzero f, this transition is avoided and replaced (presumably) by a vortex-ordering transition at much lower temperatures. We thus have studied the evolution of the dynamics for small and moderate f as the system is cooled from above T* to below. Although we do find strongly temperature-dependent slowing of the dynamics as T crosses T* and that simultaneously the dynamics becomes more complex, neither effect is anywhere nearly as dramatic as the corresponding phenomena in glass-forming liquids. At the very least, this implies that the properties of supercooled liquids must depend on more than frustration and the existence of an avoided transition.

Authors:
 [1];  [1];  [2]
  1. Stanford Univ., Stanford, CA (United States)
  2. Univ. Pierre et Marie Curie, Paris Cedex (France)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1414834
Alternate Identifier(s):
OSTI ID: 1402106
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 14; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Esterlis, Ilya, Kivelson, Steven A., and Tarjus, Gilles. Avoided criticality and slow relaxation in frustrated two-dimensional models. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.144305.
Esterlis, Ilya, Kivelson, Steven A., & Tarjus, Gilles. Avoided criticality and slow relaxation in frustrated two-dimensional models. United States. doi:10.1103/PhysRevB.96.144305.
Esterlis, Ilya, Kivelson, Steven A., and Tarjus, Gilles. Mon . "Avoided criticality and slow relaxation in frustrated two-dimensional models". United States. doi:10.1103/PhysRevB.96.144305. https://www.osti.gov/servlets/purl/1414834.
@article{osti_1414834,
title = {Avoided criticality and slow relaxation in frustrated two-dimensional models},
author = {Esterlis, Ilya and Kivelson, Steven A. and Tarjus, Gilles},
abstractNote = {Here, frustration and the associated phenomenon of “avoided criticality” have been proposed as an explanation for the dramatic relaxation slowdown in glass-forming liquids. To test this, we have undertaken a Monte Carlo study of possibly the simplest such problem, the two-dimensional XY model with frustration corresponding to a small flux f per plaquette. At f = 0, there is a Berezinskii-Kosterlitz-Thouless transition at T*, but at any small but nonzero f, this transition is avoided and replaced (presumably) by a vortex-ordering transition at much lower temperatures. We thus have studied the evolution of the dynamics for small and moderate f as the system is cooled from above T* to below. Although we do find strongly temperature-dependent slowing of the dynamics as T crosses T* and that simultaneously the dynamics becomes more complex, neither effect is anywhere nearly as dramatic as the corresponding phenomena in glass-forming liquids. At the very least, this implies that the properties of supercooled liquids must depend on more than frustration and the existence of an avoided transition.},
doi = {10.1103/PhysRevB.96.144305},
journal = {Physical Review B},
number = 14,
volume = 96,
place = {United States},
year = {2017},
month = {10}
}

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Works referenced in this record:

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
journal, November 1966


Relaxation in liquids, polymers and plastic crystals — strong/fragile patterns and problems
journal, June 1991


The uniformly frustrated two-dimensional XY model in the limit of weak frustration
journal, April 2008

  • Alba, Vincenzo; Pelissetto, Andrea; Vicari, Ettore
  • Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 17
  • DOI: 10.1088/1751-8113/41/17/175001

Theoretical perspective on the glass transition and amorphous materials
journal, June 2011


Vortices in two-dimensional superconducting weakly coupled wire networks
journal, July 1994

  • van der Zant, H. S. J.; Webster, M. N.; Romijn, J.
  • Physical Review B, Vol. 50, Issue 1
  • DOI: 10.1103/PhysRevB.50.340

Avoided critical behavior in a uniformly frustrated system
journal, March 1996

  • Chayes, L.; Emery, V. J.; Kivelson, S. A.
  • Physica A: Statistical Mechanics and its Applications, Vol. 225, Issue 1
  • DOI: 10.1016/0378-4371(95)00374-6

Slow Dynamics in the Relaxation of an Irrationally Frustrated XY Model in Two Dimensions: Analogy to Supercooled Liquids
journal, May 1997


Glassiness versus Order in Densely Frustrated Josephson Arrays
journal, January 1998


From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space
journal, May 2017


Vortex-lattice melting in two-dimensional superconducting networks and films
journal, March 1995


Glass transitions may be similar in two and three dimensions, after all
journal, February 2017


Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
journal, January 2015


Onset temperature of slow dynamics in glass forming liquids
journal, January 2000


Tuning the Fragility of a Glass-Forming Liquid by Curving Space
journal, October 2008


Observation of vortex dynamics in two-dimensional Josephson-junction arrays
journal, August 1994


Growing Static and Dynamic Length Scales in a Glass-Forming Liquid
journal, February 2010


Josephson-Junction Array in an Irrational Magnetic Field: A Superconducting Glass?
journal, August 1985


Flux-lattice melting and depinning in the weakly frustrated two-dimensional XY model
journal, May 1995


Behavior of a Josephson-junction array with golden mean frustration
journal, October 2000


A thermodynamic theory of supercooled liquids
journal, September 1995

  • Kivelson, Daniel; Kivelson, Steven A.; Zhao, Xiaolin
  • Physica A: Statistical Mechanics and its Applications, Vol. 219, Issue 1-2
  • DOI: 10.1016/0378-4371(95)00140-3

Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition
journal, October 2011


Crystalline Order in Two Dimensions
journal, December 1968


Scaling of I - V characteristics of Superconducting wire networks at irrational uniform frustration
journal, April 1992


The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
journal, December 2005


Vortex motion in two-dimensional arrays of small, underdamped Josephson junctions
journal, November 1991


Fundamental differences between glassy dynamics in two and three dimensions
journal, June 2015

  • Flenner, Elijah; Szamel, Grzegorz
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8392

Magnetic-flux dependence of the resistive transition in a square Josephson-junction array
journal, July 1988


In search of a theory of supercooled liquids
journal, November 2008

  • Kivelson, Steven A.; Tarjus, Gilles
  • Nature Materials, Vol. 7, Issue 11
  • DOI: 10.1038/nmat2304

Intrinsic Finite-Size Effects in the Two-Dimensional XY Model with Irrational Frustration
journal, October 2000


Crystallization in curved three-dimensional space
journal, December 1984


Liquid-State Properties of a One-Component Plasma
journal, February 2006


Theory of dynamic critical phenomena
journal, July 1977


Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions
journal, January 2017

  • Vivek, Skanda; Kelleher, Colm P.; Chaikin, Paul M.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
  • DOI: 10.1073/pnas.1607226113

Magnetization and universal sub-critical behaviour in two-dimensional XY magnets
journal, January 1993


Disentangling density and temperature effects in the viscous slowing down of glassforming liquids
journal, April 2004

  • Tarjus, G.; Kivelson, D.; Mossa, S.
  • The Journal of Chemical Physics, Vol. 120, Issue 13
  • DOI: 10.1063/1.1649732

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation
journal, December 2016


Josephson-Junction Arrays in Transverse Magnetic Fields
journal, November 1983


Melting of hard cubes
journal, October 1998


Flux-lattice melting in thin-film superconductors
journal, August 1980


Mermin–Wagner fluctuations in 2D amorphous solids
journal, January 2017

  • Illing, Bernd; Fritschi, Sebastian; Kaiser, Herbert
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
  • DOI: 10.1073/pnas.1612964114

Frustrated two-dimensional Josephson junction array near incommensurability
journal, May 2004


Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold
journal, March 2010


Direct Observation of Vortex Dynamics in Superconducting Films with Regular Arrays of Defects
journal, November 1996


Theoretical interpretation of resistive transition data from arrays of superconducting weak links
journal, January 1983


Current-voltage scaling of a Josephson-junction array at irrational frustration
journal, October 1996


Curvature-induced frustration in the X Y model on hyperbolic surfaces
journal, June 2009


Dynamics of a monodisperse Lennard-Jones system on a sphere
journal, February 2014