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Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics
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10.1063/1.4809741
/content/aip/journal/jcp/138/22/10.1063/1.4809741
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/22/10.1063/1.4809741
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A section of the phase diagram for the mixture (2, 3, 4) on a Bethe lattice with connectivity = 5. Thick lines represent discontinuous liquid-glass and glass-glass transitions while thin dashed lines correspond to continuous liquid-glass transition. For = 0.24 there is only one glass phase, while for = 0.3 and = 0.34 there are two glass phases. For = 0.34 the discontinuous glass-glass transition is disconnected from the liquid phase.

Image of FIG. 2.
FIG. 2.

Higher-order singularities in the mixture (2, 3, 4) on a Bethe lattice with = 5. The transition lines corresponding to generic and degenerate cusp bifurcations are denoted with and , respectively. They coalesce smoothly in a degenerate swallowtail singularity. The dashed and dotted curves belong to the unstable branches of the transition lines.

Image of FIG. 3.
FIG. 3.

The order parameter, Φ, representing the fraction of frozen spins vs temperature, , at = 0.32 and for several values of in a mixture (2, 3, 4) with = 5.

Image of FIG. 4.
FIG. 4.

A section of the phase diagram for the mixture = (2, 5, 7) on a Bethe lattice with connectivity = 12 for = 0.4, 0.52, 0.6, and 0.68. The full lines represent discontinuous transitions while the dots correspond to higher-order singularities with and structures, respectively denoted with and . Notice that for = 0.68 the glass-glass transition line is disconnected from the liquid phase.

Image of FIG. 5.
FIG. 5.

The order parameter, Φ, representing the fraction of frozen spins vs temperature, , at = 0.68 and for several values of , in the (2, 5, 7) mixture with = 12. The double jump of Φ for = 0.74, 0.76, and 0.78 corresponds to a discontinuous liquid-glass transition followed by a glass-glass transition upon lowering the temperature.

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/content/aip/journal/jcp/138/22/10.1063/1.4809741
2013-06-12
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/22/10.1063/1.4809741
10.1063/1.4809741
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