TY - JOUR

T1 - Vortex statistics in a disordered two-dimensional XY model

AU - Tang, Lei-Han

N1 - Publisher copyright:
© 1996 American Physical Society

PY - 1996/8/1

Y1 - 1996/8/1

N2 - The equilibrium behavior of vortices in a classical two-dimensional (2D) XY
model with uncorrelated random phase shifts is investigated. The model
describes Josephson-junction arrays with positional disorder and has
ramifications in a number of other bond-disordered 2D systems. The
vortex Hamiltonian is that of a Coulomb gas in a background of quenched
random dipoles, which is capable of forming either a dielectric
insulator or a plasma. We confirm a recent suggestion by Nattermann,
Scheidl, Korshunov, and Li [J. Phys. (France) I 5, 565 (1995)] and by Cha and Fertig [Phys. Rev. Lett. 74,
4867 (1995)] that, when the variance σ of random phase shifts is
sufficiently small, the system is in a phase with quasi-long-range order
at low temperatures, without a reentrance transition. This conclusion
is reached through a nearly exact calculation of the single-vortex free
energy and a Kosterlitz-type renormalization group analysis of screening
and random polarization effects from vortex-antivortex pairs. There is a
critical disorder strength σc, above which the system is in the paramagnetic phase at any nonzero temperature. The value of σc is found not to be universal, but generally lies in the range 0<σc<π/8.
In the ordered phase, vortex pairs undergo a series of spatial and
angular localization processes as the temperature is lowered. This
behavior, which is common to many glass-forming systems, can be
quantified through approximate mappings to the random energy model and
to the directed polymer on the Cayley tree. Various critical properties
at the order-disorder transition are calculated.

AB - The equilibrium behavior of vortices in a classical two-dimensional (2D) XY
model with uncorrelated random phase shifts is investigated. The model
describes Josephson-junction arrays with positional disorder and has
ramifications in a number of other bond-disordered 2D systems. The
vortex Hamiltonian is that of a Coulomb gas in a background of quenched
random dipoles, which is capable of forming either a dielectric
insulator or a plasma. We confirm a recent suggestion by Nattermann,
Scheidl, Korshunov, and Li [J. Phys. (France) I 5, 565 (1995)] and by Cha and Fertig [Phys. Rev. Lett. 74,
4867 (1995)] that, when the variance σ of random phase shifts is
sufficiently small, the system is in a phase with quasi-long-range order
at low temperatures, without a reentrance transition. This conclusion
is reached through a nearly exact calculation of the single-vortex free
energy and a Kosterlitz-type renormalization group analysis of screening
and random polarization effects from vortex-antivortex pairs. There is a
critical disorder strength σc, above which the system is in the paramagnetic phase at any nonzero temperature. The value of σc is found not to be universal, but generally lies in the range 0<σc<π/8.
In the ordered phase, vortex pairs undergo a series of spatial and
angular localization processes as the temperature is lowered. This
behavior, which is common to many glass-forming systems, can be
quantified through approximate mappings to the random energy model and
to the directed polymer on the Cayley tree. Various critical properties
at the order-disorder transition are calculated.

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U2 - 10.1103/PhysRevB.54.3350

DO - 10.1103/PhysRevB.54.3350

M3 - Journal article

SN - 2469-9950

VL - 54

SP - 3350

EP - 3366

JO - Physical Review B

JF - Physical Review B

IS - 5

ER -