TY - JOUR

T1 - Phase diagrams for the randomly diluted resistor network and XY model

AU - Harris, A. Brooks

AU - Aharony, Amnon

PY - 1989

Y1 - 1989

N2 - The randomly diluted resistor network and XY model at low temperature T are studied near the d-dimensional percolation threshold using the expansion, where =6-d. The series expansion of the inverse susceptibility in powers of T for the XY model is identical to that of the appropriate resistive inverse susceptibility in powers of 0-1, where 0 is the conductance of a bond. However, the temperature-dependent critical concentration pc(T) for the XY model has no analog in the resistor network, where pc clearly does not depend on 0. This distinction arises from a rather subtle difference between the Fourier component representation of the Gaussian model for the resistor network and that of the bounded potential energy associated with the XY model. We introduce a family of models which provides a smooth interpolation between these two models and show that the phase boundary for the XY model satisfies certain simple self-consistency checks involving other susceptibilities. In particular we provide the first explicit calculation of the universal crossover function to finite temperature of the dilute XY model.

AB - The randomly diluted resistor network and XY model at low temperature T are studied near the d-dimensional percolation threshold using the expansion, where =6-d. The series expansion of the inverse susceptibility in powers of T for the XY model is identical to that of the appropriate resistive inverse susceptibility in powers of 0-1, where 0 is the conductance of a bond. However, the temperature-dependent critical concentration pc(T) for the XY model has no analog in the resistor network, where pc clearly does not depend on 0. This distinction arises from a rather subtle difference between the Fourier component representation of the Gaussian model for the resistor network and that of the bounded potential energy associated with the XY model. We introduce a family of models which provides a smooth interpolation between these two models and show that the phase boundary for the XY model satisfies certain simple self-consistency checks involving other susceptibilities. In particular we provide the first explicit calculation of the universal crossover function to finite temperature of the dilute XY model.

UR - http://www.scopus.com/inward/record.url?scp=4244054292&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.40.7230

DO - 10.1103/PhysRevB.40.7230

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:4244054292

SN - 0163-1829

VL - 40

SP - 7230

EP - 7238

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 10

ER -