Defect energy of infinite-component vector spin glasses

Abstract

We compute numerically the zero temperature defect energy, Delta E, of the vector spin glass in the limit of an infinite number of spin components m, for a range of dimensions 2 <= d <= 5. Fitting to Delta E ~ L^theta, where L is the system size, we obtain: theta = -1.54 (d=2), theta = -1.04 (d=3), theta = -0.67 (d=4) and theta = -0.37 (d=5). These results show that the lower critical dimension, d_l (the dimension where theta changes sign), is significantly higher for m=infinity than for finite m (where 2 < d_l < 3).

4 pages, 5 figures

References in corpus (3)

• Single spin- and chiral-glass transition in vector spin glasses in three-dimensions
• Generalised Bose-Einstein phase transition in large-$m$ component spin glasses
• Spin glasses in the limit of an infinite number of spin components

Cited by in corpus (6)

• One-dimensional infinite component vector spin glass with long-range interactions
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Ground States and Defect Energies of the Two-dimensional XY Spin Glass from a Quasi-Exact Algorithm
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Genetic embedded matching approach to ground states in continuous-spin systems
• The m-component spin glass on a Bethe lattice