TY - JOUR

T1 - Exact renormalization analysis of a self-similar phase diagram with upsilon points for an Ising model

AU - Sasaki, Kazuo

PY - 1999/11

Y1 - 1999/11

N2 - The ground-state phase diagram is analyzed for a one-dimensional Ising model with long range interaction in the presence of uniform and staggered magnetic fields; the interaction is antiferromagnetic and its strength decays exponentially with distance. The exact renormalization formulas for the interactions between interfaces are derived, which is used to calculate the phase diagram hierarchically. The phase diagram is self-similar, and it contains upsilon points and devil's staircases; this agrees with the result of Aubry, Axel and Vallet [J. Phys. C 18 (1985) 753] for an equivalent, model obtained by a different method. A simple "phase rule" presenting what kind of phases appear and how they are located in the phase diagram is derived. The application of this rule to the phase diagram of betaine calcium chloride dihydrate is discussed.

AB - The ground-state phase diagram is analyzed for a one-dimensional Ising model with long range interaction in the presence of uniform and staggered magnetic fields; the interaction is antiferromagnetic and its strength decays exponentially with distance. The exact renormalization formulas for the interactions between interfaces are derived, which is used to calculate the phase diagram hierarchically. The phase diagram is self-similar, and it contains upsilon points and devil's staircases; this agrees with the result of Aubry, Axel and Vallet [J. Phys. C 18 (1985) 753] for an equivalent, model obtained by a different method. A simple "phase rule" presenting what kind of phases appear and how they are located in the phase diagram is derived. The application of this rule to the phase diagram of betaine calcium chloride dihydrate is discussed.

KW - Devil's staircase

KW - Ising model

KW - Phase diagram

KW - Renormalization

KW - Upsilon point

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U2 - 10.1143/JPSJ.68.3562

DO - 10.1143/JPSJ.68.3562

M3 - Article

AN - SCOPUS:0033275632

VL - 68

SP - 3562

EP - 3574

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 11

ER -