TY - JOUR

T1 - Phase transitions on fractals. I. Quasi-linear lattices

AU - Gefen, Y.

AU - Aharony, A.

AU - Mandelbrot, B. B.

PY - 1983/4/21

Y1 - 1983/4/21

N2 - Magnetic spin models and resistor networks are studied on certain self-similar fractal lattices, which are described as ’quasi-linear’, because they share a significant property of the line: Finite portions can be isolated from the rest by removal of two points (sites). In all cases, there is no long-range order at finite temperature. The transition at zero temperature has a discontinuity in the magnetisation, and the associated magnetic exponent is equal to the fractal dimensionality, D. When the lattice reduces to a non-branching curve the thermal exponent v-1=y is equal to D. When the lattice is a branching curve, y is related, respectively, to the dimensionality of the single-channel segments of the curve (for the Ising model), or to the exponent describing the resistivity (for models with continuous spin symmetry).

AB - Magnetic spin models and resistor networks are studied on certain self-similar fractal lattices, which are described as ’quasi-linear’, because they share a significant property of the line: Finite portions can be isolated from the rest by removal of two points (sites). In all cases, there is no long-range order at finite temperature. The transition at zero temperature has a discontinuity in the magnetisation, and the associated magnetic exponent is equal to the fractal dimensionality, D. When the lattice reduces to a non-branching curve the thermal exponent v-1=y is equal to D. When the lattice is a branching curve, y is related, respectively, to the dimensionality of the single-channel segments of the curve (for the Ising model), or to the exponent describing the resistivity (for models with continuous spin symmetry).

UR - http://www.scopus.com/inward/record.url?scp=0001532780&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/16/6/021

DO - 10.1088/0305-4470/16/6/021

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AN - SCOPUS:0001532780

SN - 0305-4470

VL - 16

SP - 1267

EP - 1278

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 6

ER -