7 3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

Juan J. Ruiz-lorenzo(c

Published Jan 1, 2008• 9 citations

OpenAlex

Abstract

Related papers

3D spin glass and 2D ferromagneticXYmodel: a comparison

D. Íñiguez, Enzo Marinari, Giorgio Parisi A +1 more

arXiv:cond-mat/9707050Journal of Physics A Mathematical and GeneralNov 7, 199724 citations

Phase Transition of Ising Spin Glass Models in Two Dimensions

Michinori Shiomi, Fumitaka Matsubara, Takayuki Shirakura

We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy $\overline{\Delta F(T)}$ and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, $\overline{\Delta F(T)}$ at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution, $\overline{\Delta F(T)}$ decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .

Journal of the Physical Society of JapanSep 1, 200010 citations

Reexamination of the SG Transition in the Two-Dimensional ±JIsing Model

Takayuki Shirakura, Fumitaka Matsubara

Using the exchange Monte Carlo method, we reexamine the ± J Ising spin glass (SG) transition in two dimensions. We calculate the SG susceptibility, the Binder cumulant and the distribution function of spin overlap at low temperatures. In contrast to our expectations, better finite-size scaling plots are obtained for a finite, nonzero transition temperature than for a zero transition temperature.

Journal of the Physical Society of JapanOct 15, 199616 citations

Lower Critical Dimension of the XY Spin-Glass Model

J. Maucourt, Daniel R. Grempel

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

Critical behaviour of the four-dimensional spin glass in magnetic field

Enzo Marinari, C. Naitza, Francesco Zuliani

arXiv:cond-mat/9802224Journal of Physics A Mathematical and GeneralJul 31, 199825 citations

A new method to calculate the spin-glass order parameter of the two-dimensional ±JIsing model

Hidetsugu Kitatani, Akira Sinada

arXiv:cond-mat/9908370Journal of Physics A Mathematical and GeneralMay 5, 20009 citations

7 3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

Juan J. Ruiz-lorenzo(c

Published Jan 1, 2008• 9 citations

OpenAlex

Abstract

Related papers

3D spin glass and 2D ferromagneticXYmodel: a comparison

D. Íñiguez, Enzo Marinari, Giorgio Parisi A +1 more

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyse similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behaviour of the XY model is fully compatible with the Kosterlitz - Thouless scenario. Finite-size effects have to be dealt with carefully in order to differentiate between two very different physical pictures that can look very similar.We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyse similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behaviour of the XY model is fully compatible with the Kosterlitz - Thouless scenario. Finite-size effects have to be dealt with carefully in order to differentiate between two very different physical pictures that can look very similar.

arXiv:cond-mat/9707050Journal of Physics A Mathematical and GeneralNov 7, 199724 citations

Phase Transition of Ising Spin Glass Models in Two Dimensions

Michinori Shiomi, Fumitaka Matsubara, Takayuki Shirakura

We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy $\overline{\Delta F(T)}$ and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, $\overline{\Delta F(T)}$ at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution, $\overline{\Delta F(T)}$ decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy $\overline{\Delta F(T)}$ and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution, $\overline{\Delta F(T)}$ at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution, $\overline{\Delta F(T)}$ decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .

Journal of the Physical Society of JapanSep 1, 200010 citations

Reexamination of the SG Transition in the Two-Dimensional ±JIsing Model

Takayuki Shirakura, Fumitaka Matsubara

Journal of the Physical Society of JapanOct 15, 199616 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

Critical behaviour of the four-dimensional spin glass in magnetic field

Enzo Marinari, C. Naitza, Francesco Zuliani

We present numerical simulations of the four-dimensional Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite-size effects, suggest the existence of a spin-glass phase transition. We present a preliminar determination of critical exponents. We discuss spin-glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite-size effects, and the behaviour of the disorder-dependent and integrated probability distributions.We present numerical simulations of the four-dimensional Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite-size effects, suggest the existence of a spin-glass phase transition. We present a preliminar determination of critical exponents. We discuss spin-glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite-size effects, and the behaviour of the disorder-dependent and integrated probability distributions.

arXiv:cond-mat/9802224Journal of Physics A Mathematical and GeneralJul 31, 199825 citations

A new method to calculate the spin-glass order parameter of the two-dimensional ±JIsing model

Hidetsugu Kitatani, Akira Sinada

A new method to numerically calculate the n th moment of the spin overlap of the two-dimensional ± J Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the n th moment of the spin overlap can be calculated as a simple average of the n th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, L , up to L = 23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about 10 5 bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of T c is strongly affected by the corrections to scaling within the present data ( L ⩽ 23). Thus, there still remains the possibility that T c = 0, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.A new method to numerically calculate the n th moment of the spin overlap of the two-dimensional ± J Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the n th moment of the spin overlap can be calculated as a simple average of the n th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, L , up to L = 23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about 10 5 bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of T c is strongly affected by the corrections to scaling within the present data ( L ⩽ 23). Thus, there still remains the possibility that T c = 0, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.

arXiv:cond-mat/9908370Journal of Physics A Mathematical and GeneralMay 5, 20009 citations

We examine the phase transition of Ising spin glass models in two dimensions (2D), calculating complementary two quantities, i.e., the interface free energy

\overline{\Delta F(T)}

and the Binder parameter g L , on finite L × L ( L ≤24) lattices at very low temperatures T . We find that these quantities exhibit quite different features depending on the distribution of bonds. For the ± J distribution,

\overline{\Delta F(T)}

at very low temperatures slightly increases with L and g L intersect at T ∼0.25 J . These results suggest a non-zero temperature phase transition, T c ≠0. On the other hand, for the Gaussian distribution,

\overline{\Delta F(T)}

decreases as L increases even at T = 0 and g L for different L converges to unity at T = 0. These results confirm the assumption of the zero temperature phase transition, T c = 0. Finite-size scaling analyses support those results. Thus we suggest that, in 2D, the existence of a finite-temperature phase transition depends on the distribution of bonds and it exists when the bond distribution is ± J .

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.