Ordering of the Heisenberg Spin Glass in High Dimensions

Abstract

Ordering of the Heisenberg spin glass with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations in four and five dimensions. Ordering of the mean-field Heisenberg spin-glass is also studied for comparison. Particular attention is paid to the nature of the spin-glass and the chiral-glass orderings. Our numerical data suggest that, in five dimensions, the model exhibits a single spin-glass transition at a finite temperature, where the spin-glass order accompanying the simultaneous chiral-glass order sets in. In four dimensions, by contrast, the model exhibits a chiral-glass transition at a finite temperature, not accompanying the standard spin-glass order. The critical region associated with the chiral-glass transition, however, is very narrow, suggesting that dimension four is close to the marginal dimensionality.

arXiv comment18 pages, 12 figures

References in corpus (12)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Dynamical simulation of spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses
• Spin-Glass and Chiral-Glass Transitions in a $\pm J$ Heisenberg Spin-Glass Model in Three Dimensions
• Nature of the ordering of the three-dimensional XY spin glass
• Stiffness of the Heisenberg Spin-Glass Model at Zero- and Finite-Temperatures in Three Dimensions
• Ordering of the three-dimensional Heisenberg spin glass in magnetic fields
• How the Replica-Symmetry-Breaking Transition Looks Like in Finite-Size Simulations
• Monte Carlo Studies of the Ordering of the Three-Dimensional Isotropic Heisenberg Spin Glass in Magnetic Fields
• Numerical simulations on the 4d Heisenberg spin glass
• Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures

Cited by in corpus (14)

• Chirality scenario of the spin-glass ordering
• Nature of the phase transition of the three-dimensional isotropic Heisenberg spin glass
• Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass
• Chiral susceptibility in canonical spin glass and reentrant alloys from Hall effect measurements
• Replica symmetry breaking transition of the weakly anisotropic Heisenberg spin glass in magnetic fields
• Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields
• Spin-chirality decoupling in Heisenberg spin glasses and related systems
• Generalised Bose-Einstein phase transition in large-$m$ component spin glasses
• Ordering of the Heisenberg spin glass in two dimensions
• Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order
• Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Ordering of the Heisenberg spin glass in four dimensions
• Spin and chirality orderings of the one-dimensional Heisenberg spin glass with the long-range power-law interaction
• Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions