The Effect of Size on Spin Glass Systems

Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility, finite-size correlation length, and the Binder ratio is performed to try to verify a recent proposal in which for large system sizes and finite but low temperatures the effective critical exponents are identical to the critical exponents of the two-dimensional Ising spin glass with Gaussian interactions. Our results show that with present system sizes the recently proposed scenario, in which the two-dimensional Ising spin glass with bimodally distributed interactions is in the same universality class as the model with Gaussian-distributed disorder at low but finite temperatures, cannot be reliably proven.Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility, finite-size correlation length, and the Binder ratio is performed to try to verify a recent proposal in which for large system sizes and finite but low temperatures the effective critical exponents are identical to the critical exponents of the two-dimensional Ising spin glass with Gaussian interactions. Our results show that with present system sizes the recently proposed scenario, in which the two-dimensional Ising spin glass with bimodally distributed interactions is in the same universality class as the model with Gaussian-distributed disorder at low but finite temperatures, cannot be reliably proven.

arXiv:cond-mat/0609377Physical Review BJan 10, 200732 citations

Finite-size critical scaling in Ising spin glasses in the mean-field regime

Timo Aspelmeier, Helmut G. Katzgraber, Derek Larson +3 more

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

arXiv:1509.05372Physical review. EMar 14, 201621 citations

Chaotic Size Dependence in Spin Glasses

Charles M. Newman, Daniel L. Stein

Springer eBooksJan 1, 19937 citations

Window Measurements of Simulations in Random Systems

Tota Nakamura, Takayuki Shirakura

Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a subsystem located in the midst of a whole system and scale them with the correlation length estimated in the subsystem. Both equilibrium data and nonequilibrium data with different system sizes and different window sizes fall onto a single scaling function. It suggests that the correction-to-scaling terms become very small. We confirm the validity in the $\pm J$ Heisenberg spin glass model in three dimensions. The spin-glass and chiral-glass transition temperatures are estimated to be very close to each other.Numerical studies in random systems are plagued with strong finite-size effects and boundary effects. We introduce a window-measurement method as a practical solution to these difficulties. We observe physical quantities only within a subsystem located in the midst of a whole system and scale them with the correlation length estimated in the subsystem. Both equilibrium data and nonequilibrium data with different system sizes and different window sizes fall onto a single scaling function. It suggests that the correction-to-scaling terms become very small. We confirm the validity in the $\pm J$ Heisenberg spin glass model in three dimensions. The spin-glass and chiral-glass transition temperatures are estimated to be very close to each other.

arXiv:1404.7590Journal of the Physical Society of JapanDec 2, 20146 citations

\pm J

Heisenberg spin glass model in three dimensions. The spin-glass and chiral-glass transition temperatures are estimated to be very close to each other.