TY - JOUR

T1 - Interface interactions in modulated phases, and upsilon points

AU - Bassler, Kevin E.

AU - Sasaki, Kazuo

AU - Griffiths, Robert B.

PY - 1991/1/1

Y1 - 1991/1/1

N2 - Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy σ to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where σ=0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.

AB - Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy σ to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where σ=0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.

KW - Frenkel-Kontorova models

KW - Modulated phases

KW - commensurate-incommensurate transitions

KW - interface interactions

KW - interfaces

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U2 - 10.1007/BF01020859

DO - 10.1007/BF01020859

M3 - Article

AN - SCOPUS:0039852694

SN - 0022-4715

VL - 62

SP - 45

EP - 88

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -