A new method to investigate the two-point correlation function decay in a finite size random spin system and at finite temperatures is proposed. It is applicable to systems with cyclic boundary conditions and in any local or uniform magnetic field. The efficiency of this method is presented in the case of an isotropic XY spin glass model with Gaussian bond distribution in external field. Using unitary U(1) gauge transformation and operator inequalities we have obtained explicit upper bounds for generalized spin-glass susceptibility κ(T,R) that describes off-diagonal transverse magnetization in two dimensional random XY spin lattices at finite temperatures. It is found that the slowest possible decay for susceptibility in random XY spin glass is of the Kosterlitz–Thouless-type with power-law decay in 2D, and the exponential type in 1D, at low temperatures. These upper bounds rule out the possibility of the corresponding magnetic ordering in 1D and 2D isotropic XY spin glasses at finite temperatures.A new method to investigate the two-point correlation function decay in a finite size random spin system and at finite temperatures is proposed. It is applicable to systems with cyclic boundary conditions and in any local or uniform magnetic field. The efficiency of this method is presented in the case of an isotropic XY spin glass model with Gaussian bond distribution in external field. Using unitary U(1) gauge transformation and operator inequalities we have obtained explicit upper bounds for generalized spin-glass susceptibility κ(T,R) that describes off-diagonal transverse magnetization in two dimensional random XY spin lattices at finite temperatures. It is found that the slowest possible decay for susceptibility in random XY spin glass is of the Kosterlitz–Thouless-type with power-law decay in 2D, and the exponential type in 1D, at low temperatures. These upper bounds rule out the possibility of the corresponding magnetic ordering in 1D and 2D isotropic XY spin glasses at finite temperatures.

Journal of Applied PhysicsNov 15, 19941 citation

Domain wall renormalization group study of the XY model with quenched random phase shifts

Nobuhiko Akino, John Michael Kosterlitz

The $\mathrm{XY}$ model with quenched random disorder is studied by a zero-temperature domain wall renormalization group method in two dimensions (2D) and three dimensions (3D). Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents ${\ensuremath{\theta}}_{s}\ensuremath{\approx}\ensuremath{-}0.36$ in 2D and ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\ifmmode\pm\else\textpm\fi{}J \mathrm{XY}$ spin glass in 3D, we obtain a spin stiffness exponent ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain ${\ensuremath{\theta}}_{s}<0.$ Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with a length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a reentrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.The $\mathrm{XY}$ model with quenched random disorder is studied by a zero-temperature domain wall renormalization group method in two dimensions (2D) and three dimensions (3D). Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents ${\ensuremath{\theta}}_{s}\ensuremath{\approx}\ensuremath{-}0.36$ in 2D and ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\ifmmode\pm\else\textpm\fi{}J \mathrm{XY}$ spin glass in 3D, we obtain a spin stiffness exponent ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain ${\ensuremath{\theta}}_{s}<0.$ Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with a length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a reentrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

arXiv:cond-mat/0203299Physical review. B, Condensed matterAug 29, 200235 citations

The low temperature phase in the 2D quantum XY model

J. Szṅajd, J. Zittartz

Journal of Magnetism and Magnetic MaterialsFeb 1, 19920 citations

Lower Critical Dimension of the XY Spin-Glass Model

J. Maucourt, Daniel R. Grempel

We investigate the $\mathrm{XY}$ spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12$ (2D) and $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8$ (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be ${d}_{\mathrm{c}}\ensuremath{\approx}3$, rather than 4 as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition, but they are also compatible with the system being at or slightly below its lower critical dimension.We investigate the $\mathrm{XY}$ spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12$ (2D) and $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8$ (3D) strongly suggest that the lower critical dimension for spin-glass ordering may be ${d}_{\mathrm{c}}\ensuremath{\approx}3$, rather than 4 as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition, but they are also compatible with the system being at or slightly below its lower critical dimension.

arXiv:cond-mat/9709197Physical Review LettersJan 26, 199845 citations

Dynamical Gauge Theory for the $XY$ Gauge Glass ModelDynamical Gauge Theory for the $XY$ Gauge Glass Model

之康尾関, Yukiyasu Ozeki

Jan 1, 20030 citations

The

\mathrm{XY}

model with quenched random disorder is studied by a zero-temperature domain wall renormalization group method in two dimensions (2D) and three dimensions (3D). Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents ${\ensuremath{\theta}}_{s}\ensuremath{\approx}\ensuremath{-}0.36$ in 2D and ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the $\ifmmode\pm\else\textpm\fi{}J \mathrm{XY}$ spin glass in 3D, we obtain a spin stiffness exponent ${\ensuremath{\theta}}_{s}\ensuremath{\approx}+0.10$ which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain ${\ensuremath{\theta}}_{s}<0.$ Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with a length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a reentrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

We investigate the

\mathrm{XY}

spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to

L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12

(2D) and

L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8

(3D) strongly suggest that the lower critical dimension for spin-glass ordering may be ${d}_{\mathrm{c}}\ensuremath{\approx}3$, rather than 4 as is commonly believed. Our 3D data favor the scenario of a low but finite spin-glass ordering temperature below the chiral transition, but they are also compatible with the system being at or slightly below its lower critical dimension.

Dynamical Gauge Theory for the

XY

Gauge Glass Model