History-dependent phase transition character.
Journal
The European physical journal. E, Soft matter
ISSN: 1292-895X
Titre abrégé: Eur Phys J E Soft Matter
Pays: France
ID NLM: 101126530
Informations de publication
Date de publication:
23 Aug 2022
23 Aug 2022
Historique:
received:
23
05
2022
accepted:
26
07
2022
entrez:
23
8
2022
pubmed:
24
8
2022
medline:
24
8
2022
Statut:
epublish
Résumé
We consider history-dependent behavior in domain-type configurations in orientational order that are formed in configurations reached via continuous symmetry-breaking phase transitions. In equilibrium, these systems exhibit in absence of impurities a spatially homogeneous order. We focus on cases where domains are formed via (i) Kibble-Zurek mechanism in fast enough quenches or by (ii) Kibble mechanism in strongly supercooled phases. In both cases, domains could be arrested due to pinned topological defects that are formed at domain walls. In systems exhibiting polar or quadrupolar order, point and line defects (disclinations) dominate, respectively. In particular, the disclinations could form complex entangled structures and are more efficient in stabilizing domains. Domain patterns formed by fast quenches could be arrested by impurities imposing a strong enough random-field type disorder, as suggested by the Imry-Ma theorem. On the other hand, domains formed in supercooled systems could be also formed if large enough energy barriers arresting domains are established due to large enough systems' stiffness. The resulting effective interactions in established domain-type patterns could be described by random matrices. The resulting eigenvectors reveal expected structural excitations formed in such structures. The most important role is commonly played by the random matrix largest eigenvector. Qualitatively different behavior is expected if this eigenvector exhibits a localized or extended character. In the former case, one expects a gradual, non-critical-type transition into a glass-type structure. However, in the latter case, a critical-like phase behavior could be observed.
Identifiants
pubmed: 35997865
doi: 10.1140/epje/s10189-022-00221-2
pii: 10.1140/epje/s10189-022-00221-2
pmc: PMC9399213
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
70Subventions
Organisme : Javna Agencija za Raziskovalno Dejavnost RS
ID : P1-0099
Organisme : Javna Agencija za Raziskovalno Dejavnost RS
ID : J1-2457
Organisme : Narodowe Centrum Nauki
ID : 2017/25/B/ ST3/02458
Organisme : Narodowe Centrum Nauki
ID : 2019/32/T/ST3/00621
Informations de copyright
© 2022. The Author(s).
Références
W.H. Zurek, Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). https://doi.org/10.1038/317505a0
doi: 10.1038/317505a0
L. Berthier, M.D. Ediger, Facets of glass physics. Phys. Today 69, 1–40 (2016). https://doi.org/10.1063/PT.3.3052
doi: 10.1063/PT.3.3052
K.H. Nagamanasa, S. Gokhale, A.K. Sood, R. Ganapathy, Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former. Nat. Phys. 11, 403–408 (2015). https://doi.org/10.1038/nphys3289
doi: 10.1038/nphys3289
M. Kleman, O.D. Lavrentovich, Soft Matter Physics: An Introduction, 1st edn. (Springer, New York, 2004)
doi: 10.1007/b97416
J. Park, T.C. Lubensky, F.C. MacKintosh, N-atic order and continuous shape changes of deformable surfaces of genus zero. Europhys. Lett. 20(3), 279–284 (1992)
doi: 10.1209/0295-5075/20/3/015
T.W.B. Kibble, Topology of cosmic domains and strings. J. Phys. A Math. Gen. 9, 1387–1398 (1976)
doi: 10.1088/0305-4470/9/8/029
A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pichler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuletić, M.D. Lukin, Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator. Nature 568, 207–211 (2019). https://doi.org/10.1038/s41586-019-1070-1
doi: 10.1038/s41586-019-1070-1
N.D. Mermin, The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591 (1979). https://doi.org/10.1103/RevModPhys.51.591
doi: 10.1103/RevModPhys.51.591
G.E. Volovik, O.D. Lavrentovich, Topological dynamics of defects: boojums in nematic drops. J. ETP 58(6), 1159–1167 (1983)
D. Svenšek, S. Žumer, Hydrodynamics of pair-annihilating disclination lines in nematic liquid crystals. Phys. Rev. E 66, 021712 (2002). https://doi.org/10.1103/PhysRevE.66.021712
doi: 10.1103/PhysRevE.66.021712
M. Svetec, S. Kralj, Z. Bradač, S. Žumer, Annihilation of nematic point defects: pre-collision and post-collision evolution. Eur. Phys. J. E 20, 71–79 (2006). https://doi.org/10.1140/epje/i2005-10120-9
doi: 10.1140/epje/i2005-10120-9
J.L. Billeter, A.M. Smondyrev, G.B. Loriot, R.A. Pelcovits, Phase-ordering dynamics of the Gay-Berne nematic liquid crystal. Phys. Rev. E 60, 6831 (1999). https://doi.org/10.1103/PhysRevE.60.6831
doi: 10.1103/PhysRevE.60.6831
Z. Bradač, S. Kralj, S. Žumer, Molecular dynamics study of the isotropic-nematic quench. Phys. Rev. E 65, 021705 (2002). https://doi.org/10.1103/PhysRevE.65.021705
doi: 10.1103/PhysRevE.65.021705
A.J. Bray, Theory of phase-ordering kinetics. Adv. Phys. 43, 357–459 (1994). https://doi.org/10.1080/00018730110117433
doi: 10.1080/00018730110117433
Y. Imry, S. Ma, Random-field instability of the ordered state of continuous symmetry. Phys. Rev. Lett 35, 1399–1401 (1975). https://doi.org/10.1103/PhysRevLett.35.1399
doi: 10.1103/PhysRevLett.35.1399
A.I. Larkin, Effect of inhomogeneities on structure of mixed state of superconductors. Sov. Phys. JETP 31, 784–791 (1970)
J. Chakrabarti, Simulation evidence of critical behavior of isotropic-nematic phase transition in a porous medium. Phys. Rev. Lett. 81, 385 (1998). https://doi.org/10.1103/PhysRevLett.81.385
doi: 10.1103/PhysRevLett.81.385
D.E. Feldman, Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors. Int. J. Mod. Phys. B 15, 2945–2976 (2001). https://doi.org/10.1142/S0217979201006641
doi: 10.1142/S0217979201006641
T. Giamarchi, P. Le Doussal, Elastic theory of flux lattices in the presence of weak disorder. Phys. Rev. B 52, 1242–1270 (1995). https://doi.org/10.1103/PhysRevB.52.1242
doi: 10.1103/PhysRevB.52.1242
A. Ranjkesh, M. Ambrožič, S. Kralj, T.J. Sluckin, Computational studies of history dependence in nematic liquid crystals in random environments. Phys. Rev. E 89, 022504 (2014). https://doi.org/10.1103/PhysRevE.89.022504
doi: 10.1103/PhysRevE.89.022504
C. Zhou, C. Reichhardt, C.J. Olson Reichhardt, I.J. Beyerlein, Dynamic phases, pinning and pattern formation for driven dislocation assemblies. Sci. Rep. 5, 8000 (2015). https://doi.org/10.1038/srep08000
doi: 10.1038/srep08000
E. Wigner, Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math. 62, 548–564 (1955). https://doi.org/10.2307/1970079
doi: 10.2307/1970079
M.L. Mehta, Random Matrices, 3rd edn. (Elsevier, Academic Press, Amsterdam, 2004)
I. Chuang, R. Durrer, N. Turok, B. Yurke, Cosmology in the laboratory: defect dynamics in liquid crystals. Science 251, 1336 (1991). https://doi.org/10.1126/science.251.4999.1336
doi: 10.1126/science.251.4999.1336
I. Chuang, B. Yurke, A.N. Pargellis, N. Turok, Coarsening dynamics in uniaxial nematic liquid crystals. Phys. Rev. E 47, 3343 (1993). https://doi.org/10.1103/PhysRevE.47.3343
doi: 10.1103/PhysRevE.47.3343
P.C. Hendry, N.S. Lawson, R.A.M. Lee, P.V.E. McClintock, C.D.H. Williams, Generation of defects in superfluid
doi: 10.1038/368315a0
M.E. Dodd, P.C. Hendry, N.S. Lawson, P.V.E. McClintock, C.D.H. Williams, Nonappearance of Vortices in fast mechanical expansions of liquid 4He through the lambda transition. Phys. Rev. Lett. 81, 3703 (1998). https://doi.org/10.1103/PhysRevLett.81.3703
doi: 10.1103/PhysRevLett.81.3703
S. Digal, R. Ray, A.M. Srivastava, Observing correlated production of defects and antidefects in liquid crystals. Phys. Rev. Lett. 83, 5030 (1999). https://doi.org/10.1103/PhysRevLett.83.5030
doi: 10.1103/PhysRevLett.83.5030
E. Kavoussanaki, R. Monaco, R.J. Rivers, Testing the Kibble-Zurek scenario with annular Josephson tunnel junctions. Phys. Rev. Lett. 85, 3452–3455 (2000). https://doi.org/10.1103/PhysRevLett.85.3452
doi: 10.1103/PhysRevLett.85.3452
Z. Bradač, S. Kralj, S. Žumer, Early stage domain coarsening of the isotropic-nematic phase transition. J. Chem. Phys. 135, 024506 (2011). https://doi.org/10.1063/1.3609102
doi: 10.1063/1.3609102
J.V. Selinger, Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals. Liq. Cryst. Rev. 6(2), 129–142 (2018). https://doi.org/10.1080/21680396.2019.1581103
doi: 10.1080/21680396.2019.1581103
P.M. Chaikin, T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995). https://doi.org/10.1017/CBO9780511813467
doi: 10.1017/CBO9780511813467
P.A. Lebwohl, G. Lasher, Nematic-liquid-crystal order—a Monte Carlo calculation. Phys. Rev. A 6, 426 (1972). https://doi.org/10.1103/PhysRevA.6.426
doi: 10.1103/PhysRevA.6.426
P. Bleher, A. Its, Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. Math. 150(2), 185–266 (1999). https://doi.org/10.48550/arXiv.math-ph/9907025
doi: 10.48550/arXiv.math-ph/9907025
M. Caselle, U. Magnea, Random matrix theory and symmetric spaces. Phys. Rep. 394(2–3), 41–156 (2004). https://doi.org/10.1016/j.physrep.2003.12.004
doi: 10.1016/j.physrep.2003.12.004
C.A. Tracy, H. Widom, Correlation functions, cluster functions, and spacing distributions for random matrices. J. Stat. Phys. 92, 809–835 (1998). https://doi.org/10.1023/A:1023084324803
doi: 10.1023/A:1023084324803
O.D. Lavrentovich, Topological defects in dispersed words and worlds around liquid crystals, or liquid crystal drops. Liq. Cryst. 24, 117–126 (1998). https://doi.org/10.1080/026782998207640
doi: 10.1080/026782998207640
S. Meiboom, J.P. Sethna, P.W. Anderson, W.F. Brinkman, Theory of the blue phase of cholesteric liquid crystals. Phys. Rev. Lett. 46, 1216 (1981). https://doi.org/10.1103/PhysRevLett.46.1216
doi: 10.1103/PhysRevLett.46.1216
P.E. Cladis, M. Kléman, Non-singular disclinations of strength S = + 1 in nematics. J. Phys. France 33, 591–598 (1972). https://doi.org/10.1051/jphys:01972003305-6059100
doi: 10.1051/jphys:01972003305-6059100
P. Oswald, P. Pieranski, Nematic and Cholesteric Liquid Crystals; Concepts and Physical Properties Illustrated by Experiments, 1st edn. (CRC Press, Boca Raton, 2005)
doi: 10.1201/9780203023013
M. Weissmann, N.V. Cohan, Density of states of a one-dimensional system with off-diagonal disorder. J. Phys. C 8(9), L145 (1975). https://doi.org/10.1088/0022-3719/8/9/017
doi: 10.1088/0022-3719/8/9/017
P.W. Anderson, Ill Consensed Matter (North Holland, Amsterdam, 1978)
P.W. Anderson, Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958). https://doi.org/10.1103/PhysRev.109.1492
doi: 10.1103/PhysRev.109.1492
R. Teerakapibal, C. Huang, A. Gujral, M.D. Ediger, L. Yu, Organic Glasses with tunable liquid-crystalline order. Phys. Rev. Lett. 120, 055502 (2018). https://doi.org/10.1103/PhysRevLett.120.055502
doi: 10.1103/PhysRevLett.120.055502
P. Poulin, H. Stark, T.C. Lubensky, D.A. Wietz, Novel colloidal interactions in anisotropic fluids. Science 275, 1770–1773 (1997). https://doi.org/10.1126/science.275.5307.1770
doi: 10.1126/science.275.5307.1770
D. Pires, J.B. Fleury, Y. Galerne, Colloid particles in the interaction field of a disclination line in a nematic phase. Phys. Rev. Lett. 98, 247801 (2007). https://doi.org/10.1103/PhysRevLett.98.247801
doi: 10.1103/PhysRevLett.98.247801
T.C. Lubensky, D. Pettey, N. Currier, H. Stark, Topological defects and interactions in nematic emulsions. Phys. Rev. E 57, 610 (1998). https://doi.org/10.1103/PhysRevE.57.610
doi: 10.1103/PhysRevE.57.610
H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, T. Kajiyama, Polymer-stabilized liquid crystal blue phases. Nat. Mater. 1, 64–68 (2002). https://doi.org/10.1038/nmat712
doi: 10.1038/nmat712
E. Karatairi, B. Rožič, Z. Kutnjak, V. Tzitzios, G. Nounesis, G. Cordoyiannis, J. Thoen, C. Glorieux, S. Kralj, Nanoparticle-induced widening of the temperature range of liquid-crystalline blue phases. Phys. Rev. E 81, 041703 (2010). https://doi.org/10.1103/PhysRevE.81.041703
doi: 10.1103/PhysRevE.81.041703
X. Wang, Y.K. Kim, E. Bukusoglu, B. Zhang, D.S. Miller, N.L. Abbott, Experimental insights into the nanostructure of the cores of topological defects in liquid crystals. Phys. Rev. Lett. 116, 147801 (2016). https://doi.org/10.1103/PhysRevLett.116.147801
doi: 10.1103/PhysRevLett.116.147801
X. Wang, D.S. Miller, E. Bukusoglu, J.J. de Pablo, N.L. Abbott, Topological defects in liquid crystals as templates for molecular self-assembly. Nat. Mater. 15, 106–112 (2016). https://doi.org/10.1038/nmat4421
doi: 10.1038/nmat4421
S. Čopar, M. Ravnik, S. Žumer, Introduction to colloidal and microfluidic nematic microstructures. Curr. Comput.-Aided Drug Des. 11(8), 956 (2021). https://doi.org/10.3390/cryst11080956
doi: 10.3390/cryst11080956
C. Chiccoli, I. Feruli, O.D. Lavrentovich, P. Pasini, S.V. Shiyanovskii, C. Zannoni, Topological defects in schlieren textures of biaxial and uniaxial nematics. Phys. Rev. E 66, 030701(R) (2002). https://doi.org/10.1103/PhysRevE.66.030701
doi: 10.1103/PhysRevE.66.030701
D.R. Nelson, Toward a tetravalent chemistry of colloids. Nano Lett. 2, 1125–1129 (2002). https://doi.org/10.1021/nl0202096
doi: 10.1021/nl0202096
V. Vitelli, A.M. Turner, Anomalous coupling between topological defects and curvature. Phys. Rev. Lett. 93, 215301 (2004). https://doi.org/10.1103/PhysRevLett.93.215301
doi: 10.1103/PhysRevLett.93.215301
M. Bowick, D.R. Nelson, A. Travesset, Curvature-induced defect unbinding in toroidal geometries. Phys. Rev. E 69, 041102 (2004). https://doi.org/10.1103/PhysRevE.69.041102
doi: 10.1103/PhysRevE.69.041102
R.L.B. Selinger, A. Konya, A. Travesset, J.V. Selinger, Monte Carlo studies of the XY model on two-dimensional curved surfaces. J. Phys. Chem. B 115, 13989–13993 (2011). https://doi.org/10.1021/jp205128g
doi: 10.1021/jp205128g
G. Skačej, C. Zannoni, Controlling surface defect valence in colloids. Phys. Rev. Lett. 100, 197802 (2008). https://doi.org/10.1103/PhysRevLett.100.197802
doi: 10.1103/PhysRevLett.100.197802
T. Lopez-Leon, V. Koning, K.B.S. Devaiah, V. Vitelli, A. Fernandez-Nieves, Frustrated nematic order in spherical geometries. Nat. Phys. 7, 391–394 (2011). https://doi.org/10.1038/nphys1920
doi: 10.1038/nphys1920
D. Jesenek, S. Kralj, R. Rosso, E.G. Virga, Defect unbinding on a toroidal nematic shell. Soft Matter 11, 2434–2444 (2015). https://doi.org/10.1039/C4SM02540G
doi: 10.1039/C4SM02540G
M. Mesarec, W. Góźdź, A. Iglič, S. Kralj, Effective topological charge cancelation mechanism. Sci. Rep. 6, 27117 (2016). https://doi.org/10.1038/srep27117
doi: 10.1038/srep27117
L. Mesarec, W. Góźdź, A. Iglič, V. Kralj Iglič, E.G. Virga, S. Kralj, Normal red blood cells’ shape stabilized by membrane’s in-plane ordering. Sci. Rep. 9, 19742 (2019). https://doi.org/10.1038/s41598-019-56128-0
doi: 10.1038/s41598-019-56128-0
L. Mesarec, A. Iglič, V. Kralj-Iglič, W. Góźdź, E.G. Virga, S. Kralj, Curvature potential unveiled topological defect attractors. Curr. Comput.-Aided Drug Des. 11(5), 539 (2021). https://doi.org/10.3390/cryst11050539
doi: 10.3390/cryst11050539
T.C. Lubensky, S.R. Renn, Twist-grain-boundary phases near the nematic–smectic-A–smectic-C point in liquid crystals. Phys. Rev. A 41, 4392 (1990). https://doi.org/10.3390/cryst11080956
doi: 10.3390/cryst11080956
L. Navailles, P. Barois, H.T. Nguyen, X-ray measurement of the twist grain boundary angle in the liquid crystal analog of the Abrikosov phase. Phys. Rev. Lett. 71, 545 (1993). https://doi.org/10.1103/PhysRevLett.71.545
doi: 10.1103/PhysRevLett.71.545
S. Kralj, S. Žumer, Saddle-splay elasticity of nematic structures confined to a cylindrical capillary. Phys. Rev. E 51, 366 (1995). https://doi.org/10.1103/PhysRevE.51.366
doi: 10.1103/PhysRevE.51.366
J. Fukuda, S. Žumer, Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal. Nat. Commun. 2, 246 (2011). https://doi.org/10.1038/ncomms1250
doi: 10.1038/ncomms1250
G. Cordoyiannis, V.S.R. Jampani, S. Kralj et al., Different modulated structures of topological defects stabilized by adaptive targeting nanoparticles. Soft Matter 9, 3956–3964 (2013). https://doi.org/10.1039/C3SM27644A
doi: 10.1039/C3SM27644A
M. Lavrič, V. Tzitzios, S. Kralj, G. Cordoyiannis, I. Lelidis, G. Nounesis, V. Georgakilas, H. Amenitsch, A. Zidanšek, Z. Kutnjak, The effect of graphene on liquid-crystalline blue phases. Appl. Phys. Lett. 103, 143116 (2013). https://doi.org/10.1063/1.4824424
doi: 10.1063/1.4824424
M. Lavrič, G. Cordoyiannis, S. Kralj, V. Tzitzios, G. Nounesis, Z. Kutnjak, Effect of anisotropic MoS
doi: 10.1364/AO.52.000E47
A. Nych, J. Fukuda, U. Ognysta, S. Žumer, I. Muševič, Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film. Nature Phys. 13, 1215–1220 (2017). https://doi.org/10.1038/nphys4245
doi: 10.1038/nphys4245