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:
-
- Stanford Univ., Stanford, CA (United States)
- 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
- Mermin, N. D.; Wagner, H.
- Physical Review Letters, Vol. 17, Issue 22
Relaxation in liquids, polymers and plastic crystals — strong/fragile patterns and problems
journal, June 1991
- Angell, C. A.
- Journal of Non-Crystalline Solids, Vol. 131-133
Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
journal, January 1975
- Villain, J.
- Journal de Physique, Vol. 36, Issue 6
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
Theoretical perspective on the glass transition and amorphous materials
journal, June 2011
- Berthier, Ludovic; Biroli, Giulio
- Reviews of Modern Physics, Vol. 83, Issue 2
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
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
Slow Dynamics in the Relaxation of an Irrationally Frustrated Model in Two Dimensions: Analogy to Supercooled Liquids
journal, May 1997
- Kim, Bongsoo; Lee, Sung Jong
- Physical Review Letters, Vol. 78, Issue 19
Glassiness versus Order in Densely Frustrated Josephson Arrays
journal, January 1998
- Gupta, Pramod; Teitel, S.; Gingras, Michel J. P.
- Physical Review Letters, Vol. 80, Issue 1
From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space
journal, May 2017
- Turci, Francesco; Tarjus, Gilles; Royall, C. Patrick
- Physical Review Letters, Vol. 118, Issue 21
Vortex-lattice melting in two-dimensional superconducting networks and films
journal, March 1995
- Franz, M.; Teitel, S.
- Physical Review B, Vol. 51, Issue 10
Glass transitions may be similar in two and three dimensions, after all
journal, February 2017
- Tarjus, Gilles
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 10
Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
journal, January 2015
- Kapfer, Sebastian C.; Krauth, Werner
- Physical Review Letters, Vol. 114, Issue 3
Onset temperature of slow dynamics in glass forming liquids
journal, January 2000
- Sastry, Srikanth
- PhysChemComm, Vol. 3, Issue 14
Tuning the Fragility of a Glass-Forming Liquid by Curving Space
journal, October 2008
- Sausset, François; Tarjus, Gilles; Viot, Pascal
- Physical Review Letters, Vol. 101, Issue 15
Observation of vortex dynamics in two-dimensional Josephson-junction arrays
journal, August 1994
- Lachenmann, S. G.; Doderer, T.; Hoffmann, D.
- Physical Review B, Vol. 50, Issue 5
Growing Static and Dynamic Length Scales in a Glass-Forming Liquid
journal, February 2010
- Sausset, François; Tarjus, Gilles
- Physical Review Letters, Vol. 104, Issue 6
Josephson-Junction Array in an Irrational Magnetic Field: A Superconducting Glass?
journal, August 1985
- Halsey, Thomas C.
- Physical Review Letters, Vol. 55, Issue 9
Zero-temperature transition and correlation-length exponent of the frustrated model on a honeycomb lattice
journal, February 2012
- Granato, Enzo
- Physical Review B, Vol. 85, Issue 5
Flux-lattice melting and depinning in the weakly frustrated two-dimensional XY model
journal, May 1995
- Hattel, So/ren A.; Wheatley, J. M.
- Physical Review B, Vol. 51, Issue 17
Behavior of a Josephson-junction array with golden mean frustration
journal, October 2000
- Kolahchi, Mohammad R.; Fazli, Hossein
- Physical Review B, Vol. 62, Issue 13
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
Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition
journal, October 2011
- Bernard, Etienne P.; Krauth, Werner
- Physical Review Letters, Vol. 107, Issue 15
Crystalline Order in Two Dimensions
journal, December 1968
- Mermin, N. D.
- Physical Review, Vol. 176, Issue 1
Scaling of I - V characteristics of Superconducting wire networks at irrational uniform frustration
journal, April 1992
- Yu, F.; Israeloff, N. E.; Goldman, A. M.
- Physical Review Letters, Vol. 68, Issue 16
The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
journal, December 2005
- Tarjus, G.; Kivelson, S. A.; Nussinov, Z.
- Journal of Physics: Condensed Matter, Vol. 17, Issue 50
Vortex motion in two-dimensional arrays of small, underdamped Josephson junctions
journal, November 1991
- Tighe, T. S.; Johnson, A. T.; Tinkham, M.
- Physical Review B, Vol. 44, Issue 18
Fundamental differences between glassy dynamics in two and three dimensions
journal, June 2015
- Flenner, Elijah; Szamel, Grzegorz
- Nature Communications, Vol. 6, Issue 1
Magnetic-flux dependence of the resistive transition in a square Josephson-junction array
journal, July 1988
- Carini, John P.
- Physical Review B, Vol. 38, Issue 1
In search of a theory of supercooled liquids
journal, November 2008
- Kivelson, Steven A.; Tarjus, Gilles
- Nature Materials, Vol. 7, Issue 11
Intrinsic Finite-Size Effects in the Two-Dimensional Model with Irrational Frustration
journal, October 2000
- Yong Park, Sung; Choi, M. Y.; Jun Kim, Beom
- Physical Review Letters, Vol. 85, Issue 16
Crystallization in curved three-dimensional space
journal, December 1984
- Straley, Joseph P.
- Physical Review B, Vol. 30, Issue 11
Liquid-State Properties of a One-Component Plasma
journal, February 2006
- Daligault, Jérôme
- Physical Review Letters, Vol. 96, Issue 6
Theory of dynamic critical phenomena
journal, July 1977
- Hohenberg, P. C.; Halperin, B. I.
- Reviews of Modern Physics, Vol. 49, Issue 3
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
Magnetization and universal sub-critical behaviour in two-dimensional XY magnets
journal, January 1993
- Bramwell, S. T.; Holdsworth, P. C. W.
- Journal of Physics: Condensed Matter, Vol. 5, Issue 4
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
Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation
journal, December 2016
- Shiba, Hayato; Yamada, Yasunori; Kawasaki, Takeshi
- Physical Review Letters, Vol. 117, Issue 24
Josephson-Junction Arrays in Transverse Magnetic Fields
journal, November 1983
- Teitel, S.; Jayaprakash, C.
- Physical Review Letters, Vol. 51, Issue 21
Flux-lattice melting in thin-film superconductors
journal, August 1980
- Fisher, Daniel S.
- Physical Review B, Vol. 22, Issue 3
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
Frustrated two-dimensional Josephson junction array near incommensurability
journal, May 2004
- Baek, In-Cheol; Yun, Young-Je; Choi, Mu-Yong
- Physical Review B, Vol. 69, Issue 17
Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold
journal, March 2010
- Sausset, François; Tarjus, Gilles; Nelson, David R.
- Physical Review E, Vol. 81, Issue 3
Direct Observation of Vortex Dynamics in Superconducting Films with Regular Arrays of Defects
journal, November 1996
- Harada, K.; Kamimura, O.; Kasai, H.
- Science, Vol. 274, Issue 5290
Theoretical interpretation of resistive transition data from arrays of superconducting weak links
journal, January 1983
- Lobb, C. J.; Abraham, David W.; Tinkham, M.
- Physical Review B, Vol. 27, Issue 1
Current-voltage scaling of a Josephson-junction array at irrational frustration
journal, October 1996
- Granato, Enzo
- Physical Review B, Vol. 54, Issue 14
Curvature-induced frustration in the model on hyperbolic surfaces
journal, June 2009
- Baek, Seung Ki; Shima, Hiroyuki; Kim, Beom Jun
- Physical Review E, Vol. 79, Issue 6
Dynamics of a monodisperse Lennard-Jones system on a sphere
journal, February 2014
- Vest, Julien-Piera; Tarjus, Gilles; Viot, Pascal
- Molecular Physics, Vol. 112, Issue 9-10
Works referencing / citing this record:
Glassy dynamics of dense particle assemblies on a spherical substrate
journal, April 2018
- Vest, Julien-Piera; Tarjus, Gilles; Viot, Pascal
- The Journal of Chemical Physics, Vol. 148, Issue 16