Defect energy of infinite-component vector spin glasses

TL;DR

This paper numerically investigates the zero-temperature defect energy of infinite-component vector spin glasses across dimensions 2 to 5, revealing a higher lower critical dimension compared to finite-component cases.

Contribution

It provides the first detailed numerical analysis of defect energies in infinite-component vector spin glasses across multiple dimensions.

Findings

The stiffness exponent theta varies from -1.54 in 2D to -0.37 in 5D.

The lower critical dimension d_l is higher for m=infinity than for finite m.

Results suggest a different phase transition behavior for infinite-component 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).