The decoupling of the glass transitions in the two-component \(p\)-spin spherical model. (English) Zbl 1457.82434
Summary: Binary mixtures of large and small particles with a disparate size ratio exhibit a rich phenomenology at their glass transition points. In order to gain insights on such systems, we introduce and study a two-component version of the \(p\)-spin spherical spin glass model. We employ the replica method to calculate the free energy and the phase diagram. We show that when the strengths of the interactions of each component are not widely separated, the model has only one glass phase characterized by the conventional one-step replica symmetry breaking. However when the strengths of the interactions are well separated, the model has three glass phases depending on the temperature and component ratio. One is the “single” glass phase in which only the spins of one component are frozen while the spins of the other component remain mobile. This phase is characterized by the one-step replica symmetry breaking. The second is the “double” glass phase obtained by cooling the single glass phase further, in which the spins of the remaining mobile component are also frozen. This phase is characterized by the two-step replica symmetry breaking. The third is also the “double” glass phase, which, however, is formed by the simultaneous freezing of the spins of both components at the same temperatures and is characterized by the one-step replica symmetry breaking. We discuss the implications of these results for the glass transitions of binary mixtures.
MSC:
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
References:
| [1] | Kirkpatrick T R and Thirumalai D 1987 Phys. Rev. Lett.58 2091 · doi:10.1103/PhysRevLett.58.2091 |
| [2] | Kirkpatrick T R and Thirumalai D 1987 Phys. Rev. B 36 5388 · doi:10.1103/PhysRevB.36.5388 |
| [3] | Berthier L and Biroli G 2011 Rev. Mod. Phys.83 587 · doi:10.1103/RevModPhys.83.587 |
| [4] | Cavagna A 2009 Phys. Rep.476 51 · doi:10.1016/j.physrep.2009.03.003 |
| [5] | Castellani T and Cavagna A 2005 J. Stat. Mech. P05012 · Zbl 1456.82490 · doi:10.1088/1742-5468/2005/05/P05012 |
| [6] | Crisanti A, Horner H and Sommers H J 1993 Z. Phys.92 257 · doi:10.1007/BF01312184 |
| [7] | Götze W 2008 Complex Dynamics of Glass-Forming Liquids: a Mode-Coupling Theory (Oxford: Oxford University Press) · Zbl 1162.82003 · doi:10.1093/acprof:oso/9780199235346.001.0001 |
| [8] | Crisanti A and Sommers H J 1992 Z. Phys. B 87 341 · doi:10.1007/BF01309287 |
| [9] | Angell C A, Ngai K L, McKenna G B, McMillan P F and Martin S W 2000 J. Appl. Phys.88 3113 · doi:10.1063/1.1286035 |
| [10] | Imhof A and Dhont J K G 1995 Phys. Rev. Lett.75 1662 · doi:10.1103/PhysRevLett.75.1662 |
| [11] | Imhof A and Dhont J K G 1995 Phys. Rev. E 52 6344 · doi:10.1103/PhysRevE.52.6344 |
| [12] | Pham K N, Puertas A M, Bergenholtz J, Egelhaaf S U, Moussaid A, Pusey P N, Schofield A B, Cates M E, Fuchs M and Poon W C K 2002 Science296 104 · doi:10.1126/science.1068238 |
| [13] | Eckert T and Bartsch E 2002 Phys. Rev. Lett.89 125701 · doi:10.1103/PhysRevLett.89.125701 |
| [14] | Pham K N, Petekidis G, Vlassopoulos D, Egelhaaf S U, Pusey P N and Poon W C K 2006 Europhys. Lett.75 624 · doi:10.1209/epl/i2006-10156-y |
| [15] | Sentjabrskaja T, Babaliari E, Hendricks J, Laurati M, Petekidis G and Egelhaaf S U 2013 Soft Matter9 4524 · doi:10.1039/c3sm27903k |
| [16] | Sentjabrskaja T, Hermes M, Poon W C K, Estrada C D, Castaneda-Priego R, Egelhaaf S U and Laurati M 2014 Soft Matter10 6546 · doi:10.1039/C4SM00577E |
| [17] | Hendricks J, Capellmann R, Schofield A B, Egelhaaf S U and Laurati M 2015 Phys. Rev. E 91 032308 · doi:10.1103/PhysRevE.91.032308 |
| [18] | Moreno A J and Colmenero J 2006 Phys. Rev. E 74 021409 · doi:10.1103/PhysRevE.74.021409 |
| [19] | Moreno A J and Colmenero J 2006 J. Chem. Phys.125 164507 · doi:10.1063/1.2361286 |
| [20] | Voigtmann Th and Horbach J 2009 Phys. Rev. Lett.103 205901 · doi:10.1103/PhysRevLett.103.205901 |
| [21] | Bosse J and Kaneko Y 1995 Phys. Rev. Lett.74 4023 · doi:10.1103/PhysRevLett.74.4023 |
| [22] | Voigtmann Th 2011 Europhys. Lett.96 36006 · doi:10.1209/0295-5075/96/36006 |
| [23] | Nya T, Ayadim A, Germain Ph and Amokrane S 2012 J. Phys.: Condens. Matter24 325106 · doi:10.1088/0953-8984/24/32/325106 |
| [24] | Schmid B and Schilling R 2010 Phys. Rev. E 81 041502 · doi:10.1103/PhysRevE.81.041502 |
| [25] | Ikeda A and Miyazaki K 2010 Phys. Rev. Lett.104 255704 · doi:10.1103/PhysRevLett.104.255704 |
| [26] | Jacquin H and van Wijland F 2011 Phys. Rev. Lett.106 210602 · doi:10.1103/PhysRevLett.106.210602 |
| [27] | Maimbourg T, Kurchan J and Zamponi F 2016 Phys. Rev. Lett.116 015902 · doi:10.1103/PhysRevLett.116.015902 |
| [28] | Crisanti A and Leuzzi L 2004 Phys. Rev. Lett.93 217203 · doi:10.1103/PhysRevLett.93.217203 |
| [29] | Crisanti A and Leuzzi L 2006 Phys. Rev. B 73 014412 · doi:10.1103/PhysRevB.73.014412 |
| [30] | Crisanti A and Leuzzi L 2007 Phys. Rev. B 76 184417 · doi:10.1103/PhysRevB.76.184417 |
| [31] | Crisanti A, Leuzzi L and Paoluzzi M 2011 Eur. Phys. J. E 34 98 · doi:10.1140/epje/i2011-11098-3 |
| [32] | Cammarota C and Biroli G 2013 J. Chem. Phys.138 12A547 · doi:10.1063/1.4790400 |
| [33] | Kob W and Berthier L 2013 Phys. Rev. Lett.110 245702 · doi:10.1103/PhysRevLett.110.245702 |
| [34] | Ozawa M, Kob W, Ikeda A and Miyazaki K 2015 Proc. Natl Acad. Sci.112 6914 · doi:10.1073/pnas.1500730112 |
| [35] | Asakura S and Oosawa F 1954 J. Chem. Phys.22 1255 · doi:10.1063/1.1740347 |
| [36] | Dijkstra M, van Roij R and Evans R 1999 Phys. Rev. E 59 5744 · doi:10.1103/PhysRevE.59.5744 |
| [37] | Bergenholtz J and Fuchs M 1999 Phys. Rev. E 59 5706 · doi:10.1103/PhysRevE.59.5706 |
| [38] | Dawson K, Foffi G, Fuchs M, Götze W, Sciortino F, Sperl M, Tartaglia P, Voigtmann T and Zaccarelli E 2000 Phys. Rev. E 63 011401 · doi:10.1103/PhysRevE.63.011401 |
| [39] | Dawson K A, Foffi G, Sciortino F, Tartaglia P and Zaccarelli E 2001 J. Phys.: Condens. Matter13 9113 · doi:10.1088/0953-8984/13/41/305 |
| [40] | Foffi G, Sciortino F, Zaccarelli E and Tartaglia P 2004 J. Phys.: Condens. Matter16 S3791 · doi:10.1088/0953-8984/16/38/002 |
| [41] | Mezard M and Parisi G 1999 J. Chem. Phys.111 1076 · doi:10.1063/1.479193 |
| [42] | Parisi G and Zamponi F 2010 Rev. Mod. Phys.82 789 · doi:10.1103/RevModPhys.82.789 |
| [43] | Charbonneau P, Kurchan J, Parisi G, Urbani P and Zamponi F 2014 J. Stat. Mech. P10009 · Zbl 1456.82236 · doi:10.1088/1742-5468/2014/10/P10009 |
| [44] | Ikeda H, Miyazaki K, Yoshino H and Ikeda A in preparation |
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